Mark the correct alternative in the following:
Let $\phi(x)=f(x)+f(2 a-x)$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a] .$ The, $\phi(x)$
A. increases on $[0, a]$
B. decreases on $[0, a]$
C. increases on $[-a, 0]$
D. decreases on $[a, 2 a]$
Formula:- (i) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on $(a, b)$ is that $f^{\prime}(x)>0$ for all $x \in(a, b)$
$\phi(x)=f(x)+f(2 a-x)$
$\Rightarrow \phi^{\prime}(x)=f^{\prime}(x)-f^{\prime}(2 a-x)$
$\Rightarrow \phi^{\prime \prime}(x)=f^{\prime \prime}(x)+f^{\prime \prime}(2 a-x)$
checking the condition
$\phi(x)$ is decreasing in $[0, a]$
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