Mathematics - Application of Derivative Question with Solution | TestHub

$f^{\prime \prime }(x)>0\Rightarrow f^{\prime }(x)$ is an increasing function.

$$\begin{array}{rl}& f^{\prime }\left(x_1\right)>f^{\prime }\left(x_2\right)\Rightarrow x_1>x_2,f^{\prime }\left(x_1\right)=f^{\prime }\left(x_2\right)\Rightarrow x_1=x_2\\ & h^{\prime }(x)=\sin 2x\left(f^{\prime }\left({\sin }^{2}x\right)-f^{\prime }\left({\cos }^{2}x\right)\right)\\ & f^{\prime }(x)=0\Rightarrow \sin 2x=0\Rightarrow x=0\\ & or{f}^{\prime }\left({\sin }^{2}x\right)=f^{\prime }\left({\cos }^{2}x\right)\Rightarrow {\sin }^{2}x={\cos }^{2}x\Rightarrow {\tan }^{2}x=1\Rightarrow x=\pm \frac{\pi }{4}\end{array}$$