Suppose that f(2) = −5, g(2) = 4, f '(2) = −2, and g'(2) = 3. Find h'(2).

Question

(a)    h(x) = 4f(x) − 3g(x)

(b)    h(x) = f(x)g(x)

(c)    h(x) = g(x) / 1+f(x)

Answer 1

(a) 4 f' - 3 g' = 4(-2) - 3(3) = -8 - 9 =-17

(b) product rule:

f g' - f' g = -5*3 - -2*4 = -15 - -8 = -7

(c) quotient rule

[ [1+g] f' - f ]/ (1+g)^2 = [ (1+4)(-2) - -5 ] /(1+4)^2

= [ -10 - -5]/5^2 = -5/25 = -1/5