Mathematics - Application of Derivative Question with Solution | TestHub

Let $y={\sin }^{4}x+{\cos }^{4}x$ $\begin{array}{rl}& \frac{dy}{dx}=4{\sin }^{3}x\cos x+4{\cos }^{3}x(-\sin x)\\ & =4\sin x\mathrm{cox}\left({\sin }^{2}x-{\cos }^{2}x\right)\\ & =(2\sin 2x)(-\cos 2x)=-\sin 4x\\ & \therefore \frac{dy}{dx}=0\Rightarrow \sin 4x=0\Rightarrow 4x=0,\pi ,2\pi ,3\pi \end{array}$ or $\mathrm{x}=0,\frac{\pi }{4},\frac{\pi }{2},\frac{3\pi }{4},\dots \dots \dots ,\Rightarrow \mathrm{x}=\frac{\pi }{4}$