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 (a)5 (b) 4 (c) 3 (d) 2.2.

Options

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

Explanation

To solve the problem, we need to find the value of the constant \( k \) in the function \( f(x) = (kx + e^x)h(x) \) given the conditions \( h(0) = 5 \), \( h'(0) = -2 \), and \( f'(0) = 18 \).

### Step-by-Step Solution:

1. **Differentiate \( f(x) \)**:
We start with the function:
\[
f(x) = (kx + e^x)h(x)
...