Calculus Problem

Question

Suppose F(2)=1,F′(2)=4,H(2)=3, and H′(2)=3.

If P(x)=F(x)⋅H(x) and Q(x)=F(x)/H(x), then find:

A. P′(2)= 

B. Q′(2)= 

Answer 1

If P(x) = F(x)⋅H(x) then use the product rule (u•v)' = u'v + uv"

So P'(2) = F'(2)•H(2) + F(2)•H'(2) = 4•3 + 1•3 = 12 + 3 = 15

If Q(x) = F(x)/H(x) then use the quotient rule (u/v)' = (u'v - uv')/v²

So Q'(2) = (F'(2)•H(2) - F(2)•H'(2))/(H(2))² = (4•3 - 1•3)/(3)² = (12 - 3)/9 = 9/9 = 1