Mathematics - Application of Derivative Question with Solution | TestHub

$f^{\prime }(x)=-3{\sin }^{2}x\cos x+6\sin x\cos x$ $\begin{array}{rl}& \forall x\in \left[0,\frac{\pi }{2}\right]\\ & =-3\sin x\cos x(\sin x-2)\end{array}$ that means, $f^{\prime }(x)\ge 0$ $\therefore f(x)$ is strictly increasing. Therefore, $f(x{)}_{\min }=f(0)=5$ and $f(x_{\text{max }}=f\left(\frac{\pi }{2}\right)=-1+3(1)+5=7$ Hence, the difference $=7-5=2$