Question

If f and g are differentiable functions for all real values of x such that f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = -2, then find h '(2) if h(x) = f(x) g(x)

13

-13

7

-7

Answer 1

The value of h'(2) is -7

Explanation:

Given,

h(x) = f(x) g(x)

Differentiating with respect to x,

h'(x) = f(x) × g'(x) + f'(x) × g(x)

Substitute x = 2,

h'(2) = f(2) × g'(2) + f'(2) × g(2) ----(1)

We have,

f(2) = 5, g(2) = 3, f '(2) = 1, g '(2) = -2,

By substituting the values in equation (1),

We get,

h'(2) = 5 × -2 + 1 × 3 = -10 + 3 = -7

Hence, LAST option is correct.