Suppose f is a differentiable function with f(0)=2 and f′(0)=5. Compute the following:h′(0) where h(x)=3x(x2+1)f(x)

Answer 1

We will have to use product rule regardless, but it looks to be easier if we distribute the 3x to the binomial first:

h(x) = (3x³ + 3x)·(f(x))

h^'(x) = (9x² + 3)·f(x) + f^'(x)·(3x³ + 3x)

h^'(0) = 3·f(0) = 6