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Let $h (x)$ be differentiable for all x and let $f (x) = (k x + e^{x}) h (x)$ where $k$ is some constant. If $h (0) = 5, h' (0) = - 2,$ and $f' (0) = 18,$ then the value of $k$ is

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2.2

answer is C.

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Detailed Solution

$f^{'} (x) = (k x + e^{x}) h^{'} (x) + h (x) (k + e^{x})$

$f^{'} (0) = h^{'} (0) + h (0) (k + 1)$

$18 = - 2 + 5 (k + 1) \Rightarrow k = 3$

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