at what value of x, the function 2x^3/3+2x^2-6x+4 is minimum​

Answers

Answer 1

Answer:

x=1

Step-by-step explanation:

We are given that

[tex]\frac{2x^3}{3}+2x^2-6x+4[/tex]

We have to find the value of x for which function is minimum.

Differentiate w.r.t x

[tex]f'(x)=2x^2+4x-6[/tex]

Substitute f'(x)=0

[tex]2x^2+4x-6=0[/tex]

[tex]x^2+2x-3=0[/tex]

[tex]x^2+3x-x-3=0[/tex]

[tex]x(x+3)-1(x+3)=0[/tex]

[tex](x-1)(x+3)=0[/tex]

[tex]x=1,-3[/tex]

Again, differentiate w.r.t x

[tex]f''(x)=4x+4[/tex]

[tex]f''(1)=4(1)+4=8>0[/tex]

[tex]f''(-3)=4(-3)+4=-8<0[/tex]

Hence, the function is minimum at x=1


Related Questions

Need help on this question, please help!

Answers

Answer:

I think it is 50

Step-by-step explanation:

You got the answer from the person on top lemme have a thank you please

All equilateral triangles are isosceles.
A. True
B. False

Answers

Answer:

A. True

Step-by-step explanation:

This statement is true. The definition of an isosceles triangle is a triangle with at least two congruent sides. Since all equilateral triangles have three congruent sides, they fit the definition of an isosceles triangle.

True my friend

jsisisosksksd

Help me find the answer to this please. And also explain how to slove these problems.​

Answers

Answer:

B and C

Step-by-step explanation:

Minimum and Maximum points occur when the gradient of the function is equal to 0. Graphically this looks like a bend such that the function dips from decreasing to increasing (the gradient goes form being negative to positive) and vice versa.

A minimum point occurs where all the nearby values are higher than that of the point in question.

A maximum point occurs where all the nearby points are lower than the point in question.

By looking at the graph, there is a maximum point around (4.5, 1.5) which is consistent with B but not A (since A talks about a minimum point)

By looking at the graph, there is a minimum point around (0.5, 1.5) which is consistent with C.

I've highlighted areas of interest below so hopefully that's helpful :>

A chain lying on the ground is 10 m long and its mass is 60 kg. How much work (in J) is required to raise one end of the chain to a height of 4 m?

Answers

Answer:

Approximately [tex]4.70 \times 10^{2}\; \rm J[/tex], assuming that [tex]g = 9.81\; \rm m \cdot s^{-2}[/tex].

Step-by-step explanation:

When the force [tex]F[/tex] is constant, moving by [tex]\Delta x[/tex] in the direction of the force would do a work of [tex]F \cdot \Delta x[/tex].

However, in this example, as an increasing portion of the chain gets lifted up, the force lifting the chain would increase in size. Hence, apply the integral form of this equation.

Let [tex]F(x)[/tex] denote the force required to lift the chain when the height above the ground is [tex]x[/tex] meters. At that moment, exactly [tex](x / 10)[/tex] of the chain would be above the ground. The mass of that much of the chain would be [tex](x / 10)\![/tex] the mass of the whole chain.

[tex]\begin{aligned}F(x) &= m(x) \cdot g \\ &= 60 \cdot \frac{x}{10} \cdot g = 6\, g\, x\end{aligned}[/tex].

Integrate with respect to [tex]x[/tex]:

[tex]\begin{aligned}\int \limits_{0}^{4} F(x) \cdot {\rm d} x &= \int \limits_{0}^{4} 6\, g\, x \cdot {\rm d} x \\ &= \left[(3\, g)\, x^{2}\right]_{x=0}^{x=4}\\ &= 48\, g \approx 4.7 \times 10^{2} \end{aligned}[/tex].

In other words, it would take approximately [tex]4.7 \times 10^{2}\; \rm J[/tex] of energy to raise one end of the chain to that height of [tex]4\; \rm m[/tex].

Plz help me with this problem I also don’t understand. Worth 12 points! Only number 8. I need help with.

Answers

Where’s the picture ? Or the question .

Answer:

Where is question

Step-by-step explanation:

3. Brenda deposited $225 into an account that earns 7.25% compound
interest. How much will be in her account after six years?"

Answers

9514 1404 393

Answer:

  $342.43

Step-by-step explanation:

Each year, the account value is multiplied by 1 +7.25% = 1.0725. After 6 years, the value will be ...

  $225(1.0725^6) ≈ $342.43

What mathematical term describes both 5.3 and 8.2 in the expression 5.3x-8.2y+11.1?

Answers

Answer:

Step-by-step explanation:

Coefficients

The decimal numbers 5.3 and 8.2 represents the coefficient of 'x' and the coefficient of 'y', respectively.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 5.3x - 8.2y + 11.1

The number associated with x is known as the coefficient of 'x'. And the number associated with y is known as the coefficient of 'y'.

The decimal numbers 5.3 and 8.2 represents the coefficient of 'x' and the coefficient of 'y', respectively.

More about the Algebra link is given below.

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ANSWER ASAP
4 power of 3 +2(3-2).
14
16
66
68
ITS NOT 45

Answers

4(3) + 2(3-2)
4(3) + 2(1)
64 + 2
the answer is 66

Answer:

245 is the answer to the question

How many 1/4 pieces can you cut if a string is 15 ft long

Answers

Answer:

60

Step-by-step explanation:

you simply do 15 ÷ .25, which you will get 60.

Answer:

60 1/4 pieces

Step-by-step explanation:

Multiply 15 x 1/4 = 60 pieces

Can someone please answer all of these questions. im begging you please

Answers

Answer:

Step-by-step explanation:

highest temp = 5.5°C

lowest temp = -3°C

-4° < -3°, so the outside temp is colder

if a polynomial has one root in the form a+√b , it has a second root in the form of a_√b​

Answers

Answer:

(a - √b​)

Step-by-step explanation:

Roots occur as positive and negative conjugates. Therefore, the conjugate of (a + √b) is (a - √b)

Heyy can someone help me ¿? ;-; is for today ;-;


Zuleima puts her pebbles on the table. Make groups of 3 and have 1 left. Then make groups of 5 and have 2 left. How many stones does Zuleima have?

Answers

Step-by-step explanation:

she has 3 because she make group of five n have one and then make a group of five and had two, so add two plus one it will give u three

The seats are divided into 40 sections. If hats are to be given in only 5 sections, what is the probability of a guest sitting in a winning section? Record your answer as a fraction in simplest form.

Answers

Answer:

P=(Probablility of a guest sitting in a section that gets a hat) =number of ways it can happen/total number of outcomes. =5/40= 1/8

Step-by-step explanation:

The probability of a guest sitting in a winning section is 1/8.

What is probability?

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Given, The seats are divided into 40 sections and hats are to be given in only 5 sections.

Here, N(S) = 40 and N(H) = 5.

Therefore, We know, P(H) = N(H)/N(S).

P(H) = 5/40.

P(H) = 1/8.

Some more concepts of probability are, Conditional probability,

A term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

learn more about probability here :

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katy desea alquilar un barca y gastar por menos $54. El barco cuesta $7 por hora y katy tiene un cupom de descuento de $9 dolares. ¿por cuántas horas podria katy alquilar el barc​

Answers

Answer:

9 horas

Explanation:

$63 por 9 horas

Cupom de descuento de $9

$63 - $9 = $54


Anthony borrowed $18,800 at 6% simple interest for 4 months. Determine the amount of interest.

Answers

First, converting R percent to r a decimal
r = R/100 = 6%/100 = 0.06 per year,
putting time into years for simplicity,
4 months ÷ 12 months/year = 0.333333 years,
then, solving our equation

I = $ 376.00

I = 18800 × 0.06 × 0.333333 = 375.999624
I = $ 376.00

The simple interest accumulated
on a principal of $ 18,800.00
at a rate of 6% per year
for 0.333333 years (4 months) is $ 376.00.

anie spent 2.5 hours doing homework she spent 1/3 of the time on the history project she spent all remaining time writing an essay how much time did Annie spent writing the essay answer fast!!!!!!!!!!

Answers

1 hour and 40 minutes, or 100 minutes.

H) Jorge had 3 pounds of strawberries. He let his friend Matt eat 1/2 of the strawberries. How many pounds of strawberries did Matt eat? ​

Answers

Answer: Matt ate 1.5 pounds of strawberries.

Step-by-step explanation:

3 ÷ 1/2 = 1.5

Answer:

1.5 pounds

Step-by-step explanation:

Total of strawberries = 3 pounds

Mat eat half of the total of strawberries = 1/2 * 3 pounds = 1.5 pounds

Help ASAP I’ll mark brainliest

Answers

Answer: C. 254

Step-by-step explanation: All engineers is the population so this is stats and the number that chose math no matter what kind of engineer is 254

WHOEVER HELPS AND GETS THESE 3 RIGHT I WILL GIVE BRAINLY TO!!!!!!

Answers

Answer/Step-by-step explanation:

16. 4(x + 3) - 5 < 5x + 7

4x + 12 - 5 < 5x + 7

4x + 7 < 5x + 7

Collect like terms

4x - 5x < 7 - 7

-x < 0

Divide both sides by -1

x > 0

17. 24 > -3x

Divide both sides by -3

24/-3 < -3x/-3

-8 < x

x > -8

18. -5(2x - 6) + 3x < 2(2x + 1) - 11x

-10x + 30 + 3x < 4x + 2 - 11x

Add like terms

-7x + 30 < -7x + 2

-7x + 7x < -30 + 2

0 < -28

(-12,16) and (-4,-2)find the slope

Answers

Answer:

It's -9/4 or -2 1/4. please mark me brainliest <3

Step-by-step explanation:

1) label x1, y1, x2, and y2.

x1     y1       x2 y2

(-12, 16)     (-4,-2)

2) Remember the formula is y2-y1

                                               --------

                                                x2-x1

3) substitute

-2-16

--------

-4-(-12)

4) two minuses (negatives) is a positive (+)

so,

-2-16             -18

---------=       --------

-4+12               8

5) simplify

-18 divided by 2          -9

-----                          =   -------    or -2 1/4

  8 divided by 2             4

Answer:

-1.75

Step-by-step explanation:

A line passes through the point (-1,-7) and has a slope of 5
Write an equation in slope-intercept form for this line.

Answers

The answer would be y = 5x -2

Lesson 4-2
2 Fill in the boxes to find the resulting equation when 25 is subtracted from
each side. Simplify both sides of the equation,
25 + x =
25
31
25
10

Answers

Answer:

-25

Step-by-step explanation:

Given the equation 25 + x =

Subtract 25 from both sides

25 + x - 25 = 0 - 25

x = 0 - 25

x = -25

Hence the blank box will be -25

How do I solve this? please help

Answers

Answer:

4322 ft^2

Step-by-step explanation:

First, we need a formula. The formula is (50*110) - (3.14*18^2) - (4*40). The answer is 4322 ft^2 (This is the rounded answer)

Three robots go out to lunch. They decide
to share the $11.91 bill evenly. How much
does each robot pay? WHATS the equation???

Answers

$3.97 each robot has to pay and i don’t 11.91 divided by 3

Someone help me out thx:(

Answers

Answer:

kwdgejyegjyfcsudyg

Step-by-step explanation:

What is the inverse of f(x) = 2x2 -4?

Need answers asap

Answers

Answer:

Step-by-step explanation:

The function doesnt have an inverse. In order for a function to actually have an inverse, it has to pass the horizontal line test. The function above has repeating y-values because of the x^2.

With all this said, you can still find the inverse of the function as long as you restrict the domain (x-values) for the function. So, you cant consider the negative x-values.

First, replace f(x) with y and then switch the x and y variables

[tex]x=2y^2-4[/tex]

Then solve for y by adding 4 to both sides, dividing by 2, and finally taking the square root.

[tex]x+4=2y^2[/tex]

[tex]\frac{x+4}{2} =y^2[/tex]

[tex]\sqrt{\frac{x+4}{2} }=y[/tex]

Translate the given phase into an algebraic expression and simplify if possible: the quotient of -20 and -40.

Answers

Answer:

0.5

Step-by-step explanation:

-20 and -40

quotient means divide one another

-20 / -40

= 20/40

= 2/4

= 0.5

I made these into tiny tiny steps, enjoy.

The translation of  the simplified algebraic expression for "the quotient of -20 and -40" is  [tex]\dfrac{1}{2}[/tex].

A collection of constants, variables or numbers connected using one or more arithmetic operator is called an algebraic expression .

Example = 4y, 3x+4.

The quotient of -20 and -40 can be written as:

[tex]\dfrac{-20}{-40}[/tex]

The expression can be simplified in the lowest form as;

[tex]\dfrac{-20}{-40}[/tex]    =     [tex]\dfrac{1}{2}[/tex]

So, the simplified algebraic expression for "the quotient of -20 and -40" is  [tex]\dfrac{1}{2}[/tex].

Learn more about algebraic expressions here :

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Find the values of the variable and the lengths of the sides.

Answers

Answer:

C) x=8, 9, 14, 9, 7

Step-by-step explanation:

2x-7=x+1

2x-x-7+7=x-x+1+7

x=8

Explain how you can tell whether a group of ratios represents a proportional relationship

Answers

Answer:

Ratios are proportional if they represent the same relationship. One way to see if two ratios are proportional is to write them as fractions and then reduce them. If the reduced fractions are the same, your ratios are proportional

Step-by-step explanation:

thx for the free points gl

Please help me. I will award brainiest thing.

Answers

9514 1404 393

Answer:

  55°

Step-by-step explanation:

A couple of auxiliary lines can be helpful.

We see that 45° is an exterior angle to the bottom triangle, which has remote interior angles that must total 45°. This means the interior angle at bottom left must be 45° -15° = 30°.

The upper right interior angle is alternate to that, so is the same measure. The exterior angle x to the upper triangle is then the sum of the remote interior angles:

  x = 25° +30°

  x = 55°

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