Let f(x) = |sinx|. Then

Question

Let f(x) = |sinx|. Then (A) f is everywhere differentiable (B) f is everywhere continuous but not differentiable at x = nπ, n∈ Z (C) f is everywhere continuous but not differentiable at x=(2n+1) (π/2), n ∈ Z (D) None of these

Tardigrade Admin · Accepted Answer

From the graph of f(x) = |sinx|, it is clear that f(x) is continuous everywhere but not differentiable at x = nπ, n ∈ Z.

Q. Let $f (x) = ∣ s in x ∣$ . Then

$f$ is everywhere differentiable

$f$ is everywhere continuous but not differentiable at $x = nπ$ , $n \in Z$

$f$ is everywhere continuous but not differentiable at $x = (2 n + 1) \frac{π}{2}$ , $n \in Z$

None of these

From the graph of $f (x) = ∣ s in x ∣$ , it is clear that $f (x)$ is continuous everywhere but not differentiable at $x = nπ$ , $n \in Z$ .

Q. Let f(x)=∣sinx∣. Then

f is everywhere differentiable

f is everywhere continuous but not differentiable at x=nπ, n∈Z

f is everywhere continuous but not differentiable at x=(2n+1)2π​, n∈Z