Let $f: R \rightarrow R$ be a function defined by $f(x)=\max \left\{x, x^{2}\right\}$. Let $S$ denote the set of all points in $R$, where $f$ is not differentiable. Then:

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Continuity and Differentiability

Let

f : R \to R

be a function defined by

f (x) = max {x, x^{2}}

. Let

S

denote the set of all points in

R

, where

f

is not differentiable. Then:

Answer: (A)

The function

f (x) = max {x, x^{2}}

equals

x^{2}

where

x^{2} \geq x

, that is for

x \leq 0

x \geq 1

, and equals

x

0 < x < 1

. At

x = 0

the left derivative is

2 (0) = 0

while the right derivative is

1

, so

f

is not differentiable there; at

x = 1

the left derivative is

1

while the right derivative is

2 (1) = 2

, so again it fails. Hence

f

is not differentiable precisely at

{0, 1}

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Single correct option