Question

G(x) = f(x) h(x), f(2)= 6, h(2) = 2, h' (2) = 15, and f'(2) = 6. Find g' (2).
g(x)=f(x)=h(x)

Answer 1

Using the product rule, we can find the derivative of g(x) with respect to x:
g'(x) = f'(x)h(x) + f(x)h'(x)

We are given f(2) = 6, h(2) = 2, h'(2) = 15, and f'(2) = 6. To find g'(2), we plug in these values:
g'(2) = f'(2)h(2) + f(2)h'(2)
g'(2) = (6)(2) + (6)(15)
g'(2) = 12 + 90
g'(2) = 102

Therefore, g'(2) = 102.

Hope this helps