Question

Suppose
g(x) = x^2f(x)
and it is known that f(3) = 5 and f '(3) = −2. Evaluate g'(3).

Answer 1

g'(x)=(x^2)'(f(x))+(f'(x))(x^2)

g'(x)=(2x)(f(x))+(f'(x))(x^2)

for g'(3)

g'(3)=(2(3))(f(3))+(f'(3))(3^2)

g'(3)=(6)(5)+(-2)(9)

g'(3)=30-18

g'(3)=12