Question

Find all values of x for which the marginal profit is zero. Interpret your answer. (Enter your answers as a comma-separated list.)

C(x) = 5x^2; R(x) = x^3 + 7x + 18

Answer 1

I already found
Marginal Cost: 5x^2
Marginal Revenue: 3x^2+7
Marginal Profit: 2x^2-10x+7

I just need the last park for which values does it become zero. I think youre supposed to equal it to zero but I cant get it to work.

Answer 2

Profit = Revenue - Cost

Your marginal profit equation is incorrect. Double check.

Answer 3

@calculusfunctions thats x^3-5x^2+7x+18 right? or do i need to take the derivative?
also my marginal cost seems to be wrong, what about that one is incorrect?

Answer 4

actually i did subtract rev from cost to get my profit, then i took deriv to get 2x^2-10x+7

Answer 5

That is correct. That is your profit function. Marginal profit is the derivative of the profit function. The first term of your derivative is incorrect.

Answer 6

What is the derivative of x³

Answer 7

Hint: It is NOT 2x²

Answer 8

@calculusfunctions oh my i made a mistake i see, its \[3x ^{2}\]

Answer 9

Yes!!

Answer 10

now whats wrong with cost and how can I get all values of x for which the marginal profit is zero?

Answer 11

Now the marginal Profit\[P \prime (x) = 0\]Thus\[3x ^{2}-10x +7=0\]Now factor or apply the quadratic formula to solve for x. Factoring is possible so try that first.

Answer 12

@calculusfunctions im sorry i lost internet connection. I tried factoring but couldnt get it right so i just did the quadratic is it 5±2√1/3?

Answer 13

@arshia93 sorry I thought you bailed on me so i was helping someone else. The is not correct.\[3x ^{2}-10x +7=(3x -7)(x -1)\]after factoring.