JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Continuity and Differentiability

Let S be the set of all points in

(- π, π)

at which the function,

f (x) = min {sin x, cos x}

is non-differentiable. Then S is a subset of which of the following?

Answer: (B)

Solution

The graph of

min {sin x, cos x}

follows whichever curve is lower and switches between them wherever

sin x = cos x

; at each such crossing the two curves meet at a corner, and that is where the function fails to be differentiable. In

(- π, π)

the equation

tan x = 1

is solved at

x = \frac{π}{4}

and

x = - \frac{3 π}{4}

. These are the only non-differentiable points, and both lie in the set

{- \frac{3 π}{4}, - \frac{π}{4}, \frac{3 π}{4}, \frac{π}{4}}

, so

S

is a subset of it.

JEE Main · 2019 · 12 Jan 2019 · Shift 1 · Single correct option