I’m trying to find the absolute Max and min, I can’t figure out how to do the derivative, thanks
Answers
Step-by-step explanation:
Step 1: Take the First Derivative This means only differentiate once.
Disclaimer: Since absolute value only take positve outputs and quadratics only take positve outputs, we can get rid of the absolute value signs so we now have
[tex]e {}^{ {x}^{2} - 1 } [/tex]
We have the function x^2-1 composed into the function e^x.
So we use chain rule
Which states the derivative of a function composed is the
derivative of the main function times the derivative of the inside function.
So the derivative of the main function is
[tex] \frac{d}{dx} (e {}^{x} ) = e {}^{x} [/tex]
Then we replace x with x^2-1
[tex]e {}^{ {x}^{2} - 1} [/tex]
Then we take the derivative of the second function which is 2x so qe multiply them
[tex]e { }^{ {x}^{2} - 1 } 2x[/tex]
Step 2: Set the equation equal to zero.
[tex]e {}^{x {}^{2} - 1} 2x = 0[/tex]
Since e doesn't reach zero. We can just set 2x=0.
[tex]2x = 0 = x = 0[/tex]
So the critical point is 0.
Since e^x will never reach zero
Since 0 is the only critical point, this where the max or min will occur at.
Next we pick any numbergreater than zero, and plug them in the derivative function which gives us a positve number.
Any pick less than zero will give us a negative number.
Since the function is decreasing then increasing, we have a minimum.
Since 0 is the only critical point, we have a absolute minimum at 0.
To find the y coordinate, plug 0 in the orginal function.
Which gives us
[tex]e {}^{ {0}^{2} - 1 } = e {}^{ - 1} = \frac{1}{e} [/tex]
So the minimum occurs at
(0,1/e).
Related Questions
5 divided by 62.55 need help asap due today and also i cant watch ads
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Please help! It's very confusing to me
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Answer:
b. is the equation and 18 is the answer.
Step-by-step explanation:
the 9 plus b has to equal the 27
18 is the value of b.
Need help with this geometric question ASAP, Thank you
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Answer:
a. x = 9
b. GH = 30; GK = 20
Step-by-step explanation:
An angle bisector in a triangle divides the sides proportionally.
a.In this triangle, that means ...
(3x +3)/18 = (3x -7)/12
2(3x +3) = 3(3x -7) . . . . . . . multiply by 36
6x +6 = 9x -21 . . . . . . . . . eliminate parentheses
27 = 3x . . . . . . . . . . . . . . add 21 -6x
x = 9 . . . . . . . . . . . . . . . divide by 3
__
b.The segment lengths are found by substituting the value of 3x in each of the given expressions:
GH = 3x +3 = 27 +3 = 30
GK = 3x -7 = 27 -7 = 20
Prove it Step by Step. Parallelogram Based Question. I will make Brainelist + 50 points
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Answer:
(i) ABCD = ABEC
(ii) As BF || AC then BE || AC, so CE = AB.
As AB = DC, then DC = CE
(iii) ΔDGE ≠ ΔCFE so I assume there is a typing error in the question, as
ΔDGC = ΔCFE
As DC = CE (as proved in (i)), AC || BE and DG ⊥ AC and CF ⊥ BE then ΔDGC = ΔCFE
(iv) As DG ⊥ AC and CF ⊥ BE, and AC || BE, then DG || CF
(v) As AC || BE then GF || DC. As DG || CF (as proved in (iv)), then DGFC is a parallelogram.
The sum of 9 times a number and 8 is 3
Answers
Answer: 9n+8=3
Step-by-step explanation:
Let's break this down
"sum" refers to addition so we must be adding 9 times a number and 8
So far we have "9 times a number + 8"
We can use the variable, n to represent "a number"
Now we have "9 times n +8"
"times" refers to multiplication, so we should multiply 9 and n
Now we have "9n+8"
"is 3" simply means that this will equal 3
So now we have the equation 9n+8=3
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Answer:
Hi shelp >//<
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Answer:
Hi shelp >//<
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Step-by-step explanation:
enebe eeeHAHAHA
If cosθ=2/3 find cscθ using identities. This is in quad. 1.
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Step-by-step explanation:
cos θ = 2/3[tex] \quad \twoheadrightarrow\sf {cos \; \theta = \dfrac{Base}{Hypotenuse} } \\ [/tex]
Hence, base = 2 units and hypotenuse = 3 units.
[tex] \quad \twoheadrightarrow\sf { H^2 = B^2 + P^2} \\ [/tex]
[tex] \quad \twoheadrightarrow\sf { P^2 = H^2 - B^2} \\ [/tex]
[tex] \quad \twoheadrightarrow\sf { P^2 = (3)^2 - (2)^2} \\ [/tex]
[tex] \quad \twoheadrightarrow\sf { P^2 = 9- 4} \\ [/tex]
[tex] \quad \twoheadrightarrow\bf { P = \sqrt{5}} \\ [/tex]
Now, we know that :
[tex] \quad \twoheadrightarrow\sf {cosec \; \theta = \dfrac{Hypotenuse}{Perpendicular} } \\ [/tex]
[tex] \quad \twoheadrightarrow\bf{cosec \; \theta = \dfrac{3}{\sqrt{5}} } \\ [/tex]
Therefore, the required answer is 3/√5.
perform the following division: 3 3/4 ÷ 2/8
Answers
Answer:
15
Step-by-step explanation:
[tex]3\frac{3}{4} / \frac{2}{8} = \frac{15}{4} / \frac{2}{8} = \frac{15}{4} * \frac{8}{2} = \frac{120}{8} = 15[/tex]
PLEASE HELP I WILL GIVE BRAINLIEST
Answers
Answer:
20 inches²
Step-by-step explanation:
perimeter = 8 + 3 + 5 + 4
= 20 inches²
On the same coordinate plane mark all points (x y) that satisfy the rule y=3x-2 SHOW GRAPH
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Answer:
*View the attached graph*
Step-by-step explanation:
Hope it helps!
Calculate the IQR given the box plot
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Answer:
10
Step-by-step explanation:
The Interquartile Range (IQR) is the difference between Q3 and Q1.
From the diagram we see that Q1 = 40, and Q3 = 50
IQR = Q3-Q1 = 50 - 40 = 10
What is the process of writing a number as a product of several factors
Answers
Answer:
Step-by-step explanation:
you need to write out all the numbers that contain the specific number in their times tables, for example. factors of 20 are 1, 20, 4, 5, and 2 because all these numbers have 20 in their times tables.
Explain how you could find the distance between points (3,6) and (7,6) on the coordinate plane
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Answer:
Count the point on the coordinate plane to the point you want to find the distended from Still stuck? Get 1-on-1 help from an expert tutor now.
Step-by-step explanation:
What is the area of this figure?
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[tex]a \: = \: square \: area \: + \: triangle \: area \: + \: rectangle \: area \: \\ [/tex]
[tex]a \: = (3 \times 3) + ( \frac{1}{2} \times 3 \times 11) + (3 \times 11) \\ [/tex]
[tex]a = 9 + \frac{33}{2} + 33 \\ [/tex]
[tex]a = 9 + 16.5 + 33[/tex]
[tex]a = 25.5 + 33[/tex]
[tex]a = 58.5 \: \: {ft}^{2} [/tex]
three less than the product of two and a number y
can someone plssss translate that into a algebraic expression
plsss ill give you brainiac
Answers
Answer:
[tex]2y-3[/tex]
Step-by-step explanation:
It is saying to subtract 3 from the product of 2 and the variable, y.
PLEASE help me. Please. Which debates among historians over the effects of the Vietnam War did you discover in your research?
Answers
Answer:
The Domino Theory suggested that one nation becoming Communist makes it more likely that others will too. Without American involvement, the South would quickly have fallen to the North and the nation, united under Communism, would have joined the Communist bloc.
Step-by-step explanation:
E D 1389 xo С 76.2° B А Find the value of x. O 38.1 O 30.9 69 O 61.8
Answers
Based on the intersecting secants theorem, the value of x is: B. 30.9°
What is the Intersecting Secants Theorem?The intersecting secants theorem states that when two secants intersect, the measure of the angle they form is half the difference of the intercepted arcs.
Thus, based on the intersecting secants theorem, we would have the following:
x = 1/2(138 - 76.2)
x = 1/2(61.8)
x = 30.9°
Learn more about intersecting secants theorem on:
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Answer:the largest angle has a measure of _____degrees.
Answers
Answer:
depends mostly it'll b 180 degress
Step-by-step explanation:
Who is the father of maths???
Answers
Answer: Archimedes
Step-by-step explanation:
Archimedes was considered the father of mathematics, simply because he made profound advancements in both science and math. His title is purely a nickname, and not because he actually created math.
Answer:
Archimedes is known as the Father Of Mathematics
Step-by-step explanation:
What is the value of x?
Answers
Answer:
lj= lk din 30 give lj= 4✓2
and ml=x= lj cos 45
on solving x= 4✓2 cos45=4
what is the volume inside a cylinder 10ft radius 6 ft height
Answers
Answer:
1884.956ft³
Step-by-step explanation:
[tex]volume = \pi {r}^{2} h \\ = \pi \times {10ft}^{2} \times 6ft \\ = 600\pi {ft}^{3} \\ = 1884.956 {ft}^{3} [/tex]
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1 Susie wants to make some hot cereal for breakfast. The directions say to use 3 cups
of water with 1 cup of cereal to make 4 servings. Susie only wants 1 serving.
a
How much cereal should she use?
b How much water should she use?
Answers
Using proportions to relate the amount of cups needed, it is found that she should use:
a) 0.25 cups of cereal.
b) 0.75 cups of water.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, for 4 servings, 3 cups of water and 1 cup of cereal is needed. One serving is one-fourth of the amount, hence:
Item a:
1/4 x 1 = 0.25 cups of cereal.
Item b:
1/4 x 3 = 3/4 = 0.75 cups of water.
More can be learned about proportions at https://brainly.com/question/24372153
Stedents are decorating a banner to hang in the school way. The banner is 9 1/2 feet long and 2 1/2 feet wide . What is the area of the border the students are decorating?
3 4/5square feet
12 square foot
24 square feet
23 3/4square feet
Answers
Answer:
it would be 12 square feet human
Step-by-step explanation:
9 1/2+2 1/2=12 so 12 square feet
Need help please!
1.) m varies directly as a and b; m=10 when a=4 and b=7. Find m when a=11 and b=8.
2.) q varies jointly as x and y. Find q when x=2 and y=5, given that q=90 when x=3 and y=5.
3.) F varies jointly as x and y. If F=1 when x=1/2 and y=1/3, find F when x=2 and y=3.
4.) Let x be proportional to p and q^2, and inversely proportional to r^3. If x=9 when p=4, q=9, and r=3, find x if p=6, q=2, and r=5.
Answers
Answer:
4) v=kx^2/y^3
2= k(4^2)/(3^3)
2 =k16/27
k = 2(27/16) = 27/8
v = (27/8)(3^2)/(2^3 = (27/8)(9/8) = 243/64
v = 243/64 when x=3 and y=2
Step-by-step explanation:
here
F varies jointly as x and y and the value of x is 3 and y is 2.
We have given that,
1.) m varies directly as a and b m=10 when a=4 and b=7. Find m when a=11 and b=8.
What is the formula?v=kx^2/y^3
2= k(4^2)/(3^3)
2 =k(16/27)
k = 2(27/16)
k = 27/8
v = (27/8)(3^2)/(2^3)
= (27/8)(9/8)
= 243/64
v = 243/64 when x=3 and y=2.
Therefore we get the value of x is 3 and y is 2.
To learn more about the inverse value visit:
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What is an equation of the line that passes through (0, 4) and (2,8)?
Answers
Answer:
y=2x+4
Step-by-step explanation:
Hi there!
We are given the points (0, 4) and (2,8)
We want to write the equation of the line that passes through these two points
There are 3 ways to write the equation of the line, but the most common way is with slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
So, to use this way, we need to find the slope of the line
The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points
We are already given the points needed to find the slope, but let's label them to avoid any confusion
[tex]x_1=0\\y_1=4\\x_2=2\\y_2=8[/tex]
Now substitute these values into the formula.
m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m=[tex]\frac{8-4}{2-0}[/tex]
Subtract
m=[tex]\frac{4}{2}[/tex]
Divide
m=2
The slope of the line is 2
Here is the equation of the line so far:
y=2x+b
Now we need to find b
As stated before, b is the y intercept of the line, which is the point in where the line passes through the y axis; the value of x at this point is 0
One of the points we were given earlier is actually the y intercept of the line; that point is (0, 4) *notice how x=0 at this point
The value of b is the value of y at the y intercept; in this case, the value of b is 4
Substitute 4 as b into the equation
y=2x+4
Hope this helps!
See more on this topic here: https://brainly.com/question/27172025
tim drives at an average of 80km per hour for 3 hours 45 minutes. work out how many kilometres tim drives
Answers
Tim covered 21.333 kilometers
Kilometers, km covered is distance, d
d = speed / time
d = 80 / 3 hours 45 mins
Converting 45 mins to hours we have
1 hour = 60 minutes
? Hours = 45 minutes
? = 45 / 60 = 0.75
So time is 3.75 hours
d = 80 / 3.75
= 64 / 3
= 21.333km
hope it helps
Answer:
300 km
Step-by-step explanation:
Tim drives 80 km in 1 hour or 60 minutes
Tim drives in 1 minute = 80/60 km
so, tim drives in 3 hours 45 minutes ( 225 minutes)
[tex] \frac{80 \times 225}{60} [/tex]
= 300 km
Katie ate dinner at a restaurant. The bill came to $77. If she left an 18% tip, how much was the tip?
Can someone pls help me?
Answers
Answer:
$13.86
Step-by-step explanation:
Just multiply 77 by 18 percent as a decimal (.18) to get the answer, which is $13.86
Hopefully this helps- let me know if you have any questions!
How many 12 hours periods (half days) will pass after 25 hours? Enter only the whole number of period that have passed?
Answers
Answer:
2
Step-by-step explanation:
12 + 12 = 24
An envelope is 8 centimeters wide, and it measures 17 centimeters along the diagonal. How tall is the envelope? centimeters
Answers
Answer:
15cm
Step-by-step explanation:
√289-64√22515cm© the envelope is 15cm rall.
Answer:
15cm
Step-by-step explanation:
√289-64
√225
15cm
How to write 12/4 as a whole number
Answers
Answer:
3
Step-by-step explanation:
12 Divided By 4 Is 3
And 3 Is A Whole Number
Your answer is 3
Hope this helps! Please let me know if you need more help or think my answer is incorrect. Brainliest would be MUCH appreciated. Have a wonderful day!