Question

Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100

How do I simplify this so I can take the derivative

Answer 1

Profit=p(-p^2+33p+9)-9(-p^2+33p+9)+100

p(-p^2 + 33p + 9)
Just distribute the p in.

-9(-p^2 + 33p + 9)
Find the derivative of the (-p^2 + 33p + 9) and then multiply it by -9. You can distribute the -9 in at the beginning, but it's not necessary.

+100
The derivative of a consonant is 0.

I hope that helps. If you have any questions, let me know.

Answer 2

I got -3p^2+84p+298

Is this right?

Answer 3

I made a mistake it should be -296 but I do not think this is right because I know I am supposed to factor this and I cannot get it to factor.

Answer 4

That is wrong too Now I got
-3p^2+84p-288

Is this right, I cannot figure out how to factor it though

Answer 5

Yes, that's correct. To factor, you can take out a common number. (Take out a negative to make it easier to work with, too.) Try that, and see what you get.

Answer 6

I got -3(p^2-28p+96)

Now How do I factor this further I need to eventually set it equal to zero

Answer 7

Don't worry about setting it equal to 0. Since we're factoring, it is equal to 0. (You can write that = 0 in your work if you want.)

That's difficult to continue factoring. Here's a hint: 4 x 24 is 96.

Answer 8

So is it -3(p-24)(p+4)
I have to find which will give me my largest profit so I need to set them equal to zero. That would then be $24, right?
How do I determine max possible weekly profit?

Answer 9

Wait, the other one is wrong, it is
-3(p-24)(p-4).
So the max possible weekly profit is $24 dollars???

Now how do I determine the max possible weekly profit and be certain the profit is maximized?

Answer 10

Don't forget that factoring gives you the x-intercepts of an equation. Maxima are the highest and lowest y-values.

Have you learned the First Derivative Test?

Answer 11

No, But should I charge $24 to get the largest weekly profit?