Calculus Question

Question

Given that g(5) = −6 and g'(5) = 3 find f '(5), if possible. (If not possible, enter IMPOSSIBLE.) f(x) = [g(x)]3

Answer 1

Note that for the function f(x) = g(x)^3, we can find that the derivative f'(x) is equal to

f'(x) = d/dx{ g(x)^3 } = 3 g'(x) g(x)^2

We are given that g(5) = -6 and g'(5) = 3. This information is sufficient to show that

f'(5) = 3 g'(5) g(5)^2 = 3 * 3 * (-6)^2 = 9 * 36 = 324