Question

Let f(x) =max {2 sin x, 1-cos x), $xϵ(0,\pi )$, Then set of points of non-differentiability is:

• A. $\varphi$
  
• B. $\left\{\frac{\pi }{2}\right\}$
• C. $\{\pi -co{s}^{-1}\frac{3}{5}\}$
  
• D. $\left\{co{s}^{-1}\frac{3}{5}\right\}$

Answer 1

The correct option is C $\{\pi -co{s}^{-1}\frac{3}{5}\}$




$f\left(x\right)=max.2sinx,1-cosx$.
f(x) will be not differentiable at $x=\alpha$ where
$2sin\alpha =1-cos\alpha$
$\Rightarrow 4si{n}^2\alpha =1+co{s}^2\alpha -2cos\alpha$
$\Rightarrow 5co{s}^2\alpha -2cos\alpha -3=0$
$\Rightarrow (5cos\alpha +3)(cos\alpha -1)=0$
$\Rightarrow cos\alpha =\frac{-3}{5},cos\alpha =1$
$\Rightarrow \alpha =cos-1\left(\frac{-3}{5}\right)=\pi -co{s}^{-1}\left(\frac{3}{5}\right)$ . As $\alpha \ne 0$.