In (. 0 , 2 π .) , the total number of points where f(x)=max. sin x , cos ⁡ x , 1 - cos ⁡ x is not differentiable, are equal to

Question

In (. 0 , 2 π .) , the total number of points where f(x)=max. sin x , cos ⁡ x , 1 - cos ⁡ x is not differentiable, are equal to (A) 3 (B) 4 (C) 5 (D) 6

Tardigrade Admin · Accepted Answer

The graph of f(x)=max. sin x , cos â¡ x , 1 - cos â¡ x is <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-tq0xt70sp7p2.png" /> ⇒ f(x) is not differentiable at x = (π /4) , (π /2) , (5 π /3) . ⇒ f(x) is not differentiable at 3 points

Q. In $(0, 2 π)$ , the total number of points where $f (x) = ma x . {s in x, cos x, 1 - cos x}$ is not differentiable, are equal to

$3$

4

5

6

The graph of $f (x) = ma x . {s in x, cos x, 1 - cos x}$ is

$\Rightarrow$ $f (x)$ is not differentiable at $x = \frac{π}{4}, \frac{π}{2}, \frac{5 π}{3}$ .
$\Rightarrow$ $f (x)$ is not differentiable at $3$ points

Q. In (0,2π) , the total number of points where f(x)=max.{sinx,cos⁡x,1−cos⁡x} is not differentiable, are equal to

3

4

5

6

The graph of f(x)=max.{sinx,cos⁡x,1−cos⁡x} is ⇒ f(x) is not differentiable at x=4π​,2π​,35π​ . ⇒ f(x) is not differentiable at 3 points

Q. In $(0, 2 π)$ , the total number of points where $f (x) = ma x . {s in x, cos x, 1 - cos x}$ is not differentiable, are equal to

$3$

The graph of $f (x) = ma x . {s in x, cos x, 1 - cos x}$ is

$\Rightarrow$ $f (x)$ is not differentiable at $x = \frac{π}{4}, \frac{π}{2}, \frac{5 π}{3}$ .
$\Rightarrow$ $f (x)$ is not differentiable at $3$ points