Let h(x) be differentiable for all x and...

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

A

5

B

4

C

3

D

2.2

Text Solution

Verified by Experts

`f'(x)=(kx+e^(x))h'(x)+h(x)(k+e^(x))`
`f'(0)=h'(0)+h(0)(k+1)`
`"or "18=-2+5(k+1)or k=3`

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