Question

Let $f : (-1,1) \to R$ be a function defined by $f(x) = max \\{- | x |,- \sqrt{ 1- x^2} \\}$. If $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly :

• A. Three elements
• B. One element
• C. Five elements
• D. Two elements

Answer 1

Answer: (A)

Three elements

Answer 2

$f : (-1, 1) \to R$
$f(x) = \text{max} \\{- | x | , - \sqrt{1 - x^2 } \\}$
Non-derivable at $3$ points in $(-1, 1)$