# Q13

Calculus Level 3

A twice differentiable function $$f(x)$$ is defined for all real numbers and satisfies the following conditions :

$\begin{cases} f(0)=2 \\ f'(0)=-5 \\ f''(0)=3 \end{cases}$

The function $$g(x)$$ is defined by $$g(x)={ e }^{ ax }+f(x)$$ for all $$x\in R$$, where $$a$$ is a constant.

If $$g'(0)+g''(0)=0$$, then find the possible values of $$a$$.

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