Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown.

(a) Find P ‘(2). (b) Find Q'(7).

a)

P(x) = F(x)G(x)

P ‘(x) = F'(x)G(x) + F(x)G'(x)

P'(2) = F'(2)G(2) + F(2)G'(2) = 0*2 + 3*(1/2) = 3/2

b)

Q(x) = F(x)/G(x)

Q'(x) = [F ‘(x)G(x) – F(x)G ‘(x)]/(G(x))^2

Q'(7) = [F ‘(7)G(7) – F(7)G ‘(7)]/(G(7))^2

Q'(7) = [(1/4)(1) – 5*(-2/3)] / (1^2) = (1/4) + (10/3) = 43/12 = 3 7/12