Let f be a differentiable function such that f(3) = 4 and f'(3) = 5. If g(x) = x2f(x), what is the value of g'(3)?

Question

Let f be a differentiable function such that f(3) = 4 and f'(3) = 5. If g(x) = x²f(x), what is the value of g'(3)?

A) 11

B) 24

C) 30

D) 69

Answer 1

g'(x), by the product rule, is 2x f(x) +x² f'(x). When x=3, we know the values of x, f(x), x², and f'(x), so it's just arithmetic to get 2·3·4 + 9·5 = 69.