Calculus Question

Question

Given that g(8) = −5, g'(8) = 2, h(8) = 5, and h'(8) = −9 find f '(8), if possible. (If not possible, enter IMPOSSIBLE.) f(x) = g(h(x))

Answer 1

Chain rule tells us that if f(x)=g(h(x)), then f'(x) = g'(h(x)) h'(x).

So f'(8)=g'(h(8)) h'(8) = -9 g'(5), but we do not know g'(5), so there is not enough information, so you would enter impossible.