weird derivative question? stewart calculus 3.3 #54?

Question

q=f(p)

R(p)=pf(p)

a) what does it mean to say that f(20)=10,000 and f'(20)=-350?

b) find R'(20) and interpret your answer.

I have know idea of how to do this question.

I know how to take derivatives and stuff.

this question is asked after the book discussed the product and quotient rules. antiderivatives are not handled yet.

Answer 1

Best Answer

R'(p) = p f'(p) + f(p) (1)

R'(20) = 20 f'(20) + f(20) = 20 (-350) + 10000 = 3000