Largest and smallest values of marginal cost

[enchilosa]

Homework Statement

Suppose the total cost of producing x units of a certain commodity is

C(x)= (1/4*x^4) + (-37/3*x^3) + (280/2*x^2) + (1200x) + (100)

Determine the largest and the smallest values of the MARGINAL cost C'(x) for 0<x<18

The largest value of the marginal cost is _____.
The smallest value of the marginal cost is _____.

Hint. The function f(x) that you have to MIN/MAX is the derivative of cost, i.e. f(x)=C'(x)

Homework Equations

I found the derivative, which is
(x^3) - (37*x^2) + (280x) +(1200)

The Attempt at a Solution

So I found the derivative which is above and found the critical values which are x=3, x=-20, but the values must be between 0 and 18? I am not really understanding this question. please help!

 

[sprint]

is this an economics problem?

anyways to find the max or minimum (don't remember which one) set the derivative of the function equal to zero and then solve for the variable

 

[enchilosa]

is this an economics problem?

anyways to find the max or minimum (don't remember which one) set the derivative of the function equal to zero and then solve for the variable

yes, I did that and I got -3 and 20. I plugged those in back into the original equation (cost function) but the answers are incorrect.

 

[HallsofIvy]

Homework Statement

Suppose the total cost of producing x units of a certain commodity is

C(x)= (1/4*x^4) + (-37/3*x^3) + (280/2*x^2) + (1200x) + (100)

Determine the largest and the smallest values of the MARGINAL cost C'(x) for 0<x<18

The largest value of the marginal cost is _____.
The smallest value of the marginal cost is _____.

Hint. The function f(x) that you have to MIN/MAX is the derivative of cost, i.e. f(x)=C'(x)

Homework Equations

I found the derivative, which is
(x^3) - (37*x^2) + (280x) +(1200)

The Attempt at a Solution

So I found the derivative which is above and found the critical values which are x=3, x=-20, but the values must be between 0 and 18? I am not really understanding this question. please help!

Read that hint very, very carefully! In order to find max and min of MARGINAL cost, you want to find max and min of C', not C. Your derivative is f= C'= x^3- 37x^2+ 280x+ 1200 and you want to find the max and min of that so you must differentiate again and set that to 0!