If $f^{\prime \prime}(x)

Question

If $f^{\prime \prime}(x)<0 \forall x \in R$ and $g(x)=f\left(x^2-2\right)+f\left(6-x^2\right)$ then

Professor PC Thomas Classes · Answer

$f^{\prime\prime}(x)<0 \forall x\in R \Rightarrow f^{\prime}(x)$ is decreasing function and $g^{\prime}(x)=2x(f^{\prime}(x^{2}-2)-f^{\prime}(6-x^{2}))$ for $g^{\prime}(x)>0$ (i) $x>0$ and $x^{2}-2<6-x^{2}$ or (ii) $x<0$ and $x^{2}-2>6-x^{2}$