The number of points at which the function f(x)=|x - 0 .5|+|x - 1|+tanx is not differentiable in the interval (0 , 2) is/are

Question

The number of points at which the function f(x)=|x - 0 .5|+|x - 1|+tanx is not differentiable in the interval (0 , 2) is/are (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

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 .

Q. The number of points at which the function $f (x) = ∣ x - 0.5 ∣ + ∣ x - 1 ∣ + t an x$ is not differentiable in the interval $(0, 2)$ is/are

$1$

$2$

$3$

$4$

The curve will have sharp corner at $x = 0.5$ and at $x = 1$ and a point of discontinuity at $x = \frac{π}{2}$ .
Hence, total number of points where the function is not differentiable is $3$ .

Q. The number of points at which the function f(x)=∣x−0.5∣+∣x−1∣+tanx is not differentiable in the interval (0,2) is/are

1

2

3

4

The curve will have sharp corner at x=0.5 and at x=1 and a point of discontinuity at x=2π​ . Hence, total number of points where the function is not differentiable is 3 .

Q. The number of points at which the function $f (x) = ∣ x - 0.5 ∣ + ∣ x - 1 ∣ + t an x$ is not differentiable in the interval $(0, 2)$ is/are

$1$

$2$

$3$

$4$

The curve will have sharp corner at $x = 0.5$ and at $x = 1$ and a point of discontinuity at $x = \frac{π}{2}$ .
Hence, total number of points where the function is not differentiable is $3$ .