Marginal Profit

[kabraithwaite]

I have this problem for homework and I have tried several ways to get the answer but I keep getting it wrong, please help!

Problem:
The profit(in thousands of dollars) from the expenditure of x thousand dollars on advertising is given by P(x)=1000+64x-2x^2. Find the marginal profit when the expeniture is $2000.

I know the answer is 56000, but I do not know how the answer was obtained. Thanks for any help!

 

[kabraithwaite]

My work:

p=r-c
p=-2x^2+64x+1000
(-b/2a)=(-64/-4)=16

p'(x)=r'(x)-c'(x)
=2000-(1000+64x-2x^2)=-1000-64x+2x^2+2000=2x^2-64x+1000