The number of points at which the function f(x) = |x - 0.5| + |x - 1| + tan x is not differentiable in the interval (0,2) is/are

Correct answer: C. 3 The curve will have sharp corner at x = 0.5 and at x = 1 and a point of discontinuity at x = (π)/(2) . Hence, total number of points where the function is not differentiable is 3.

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Continuity and Differentiability

NTA Abhyas 2020 · Mathematics · Continuity and Differentiability

The number of points at which the function f(x) = |x - 0.5| + |x -...

The number of points at which the function

f\left(x\right) = \left|x - 0.5\right| + \left|x - 1\right| + tan x

is not differentiable in the interval

(0,2)

is/are

Options

A $1$
B $2$
C $3$
D $4$

Correct answer

C. $3$

Step-by-step solution

The curve will have sharp corner at

x = 0.5

and at

x = 1

and a point of discontinuity at

x = \dfrac{π}{2}

.
Hence, total number of points where the function is not differentiable is

3.

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