Let f (2)=2 and f '(2)=-3. Also, let g (x)=x^2 f (x). Find g '(2).

Answer 1

This problem is expecting you to use the product rule on g(x).

g'(x) = x²f'(x) + 2x f(x) -- first times derivative of 2nd plus 2nd time derivative of 1st

So, g'(2) = 2²f'(2) + 2(2) f(2) = 4(-3) + 2(2)(2) = -12+8 = -4