Question

Suppose that f and g are functions such that g(-2) = 2, f(2) = 14, g'(-2) = 1, and f '(2) = -1/16. If h(x) = f(g(x)) then the equation of the line tangent to y = h(x) at x=-2 is y =

Answer 1

By the chain rule:
h'(x) = f'(g(x))g'(x)
h'(-2) = (-1/16)(1)
h'(-2)= -1/16

slope of tangent line is -1/16
h(-2) = f(g(-2)) = 14

y-14 = -1/16(x+2)
y = -1/16x +111/8