# Suppose the marginal profit from the sale of x hundred items is:

P'(x)=4-6x=3x^2

and the profit of 0 items is -$40

A. Find the profit function.

B. Find the profit from selling 800 items

I assume the P' is 4-6x+3x^2

Then P= 4x - 3x^2 + x^3 + C

where C is the constant of integration. You have P when x=0, so C= -40

Put in x=800 and you have it.

14 years ago

8 months ago

## To find the profit function, we need to integrate the marginal profit function, P'(x), with respect to x.

A. To find the profit function, integrate P'(x):

âˆ«(4 - 6x + 3x^2) dx = 4x - 3/2x^2 + x^3/3 + C

Since the profit of 0 items is -$40, we can substitute x=0 and P= -40 into the profit function equation to solve for the constant C:

-40 = 0 + 0 + 0 + C

C = -40

Now we can substitute the value of C back into the profit function equation to get the final profit function:

P(x) = 4x - 3/2x^2 + x^3/3 - 40

B. To find the profit from selling 800 items, substitute x=800 into the profit function:

P(800) = 4(800) - 3/2(800)^2 + (800)^3/3 - 40

Calculate the expression to get the answer.