Question

If f and g are differentiable functions for all real values of x such that f(1) = 4, g(1) = 3, f '(3) = −5, f '(1) = −4, g '(1) = −3, g '(3) = 2, then find h '(1) if h(x)= f(x)/g(x)

Answer 1

h(x) = f(x)/g(x)

Use the quotient rule.

h '(x) = [g(x) f '(x) - f(x) g '(x)] / [g(x)]^2

=> h '(1) = [g(1) f '(1) - f(1) g '(1)] / [(g(1) ] ^2

h '(1) = [ 3*(-4) - 4*(-3)] / (3)^2 = [-12 + 12] / 9 = 0

Answer: 0