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) We use product rule here. P'(x) = F'(x)G(x) + F(x)G'(x).P'(2) = F'(2)G(2) + F(2)G'(2). Looking at the graph: F'(2) = 0, F(2) = 3, G'(2) = 1/2, G(2) = 2. Hence, P'(2) = (0)(2) + (3)(1/2) = 1.5.
(b) Using the quotient rule here. Q'(x) = (G(x)F'(x) - F(x)G'(x))/G(x)^2. Looking at the graph: F'(7) = 1/4, F(7) = 5, G'(7) = -3/2, G(7) = 1. Q'(7) = (1*1/4-5*(-3/2))/1^2 = 31/4 = 7.75.

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