Let `h(x)` be differentiable for all `x` and let `f(x)=(k x+e^x)h(x)` , where `k` is some constant. If `h(0)=5,h^(prime)(0)=-2,a n df^(prime)(0)=18 ,` then the value of `k` is

Options

A. 5
B. 4
C. 3
D. 2.2

Explanation

To solve the problem step-by-step, we need to differentiate the function \( f(x) = (k x + e^x) h(x) \) and then use the given values to find the constant \( k \).

### Step 1: Differentiate \( f(x) \)

Using the product rule, we differentiate \( f(x) \):

\[
f'(x) = \frac{d}{dx}[(k x + e^x) h(x)]
...