Question

If f(x) = max {$sinx$, $co{s}^{-1}x$}, then

• A. f is differentiable everywhere
• B. f is continuous everywhere but not differentiable
• C. f is discountinuous at $x=\frac{n\pi }{2}$,$n\in N$
  
• D. f is non-differentiable at $x=\frac{n\pi }{2}$, $n\in N$
  

Answer 1

The correct option is B f is continuous everywhere but not differentiable

Func is continous but not differential at A

Find A;

$co{s}^{-1}x=\sin x$

$\Rightarrow x=\cos \left(\cos \right(90-x\left)\right)$

$\Rightarrow 2x=90$

$\Rightarrow x={45}^{\circ }$