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  4. At how many points between the interval (-∞, ∞) is the function f ( x )= sin x is not differentiable.

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Q. At how many points between the interval $(-\infty, \infty)$ is the function $f ( x )=\sin x$ is not differentiable.

Continuity and Differentiability

Solution:

The function $f(x)=\sin x$ is differentiable for all $x \in R$. Therefore the number of points in the interval ($\infty, \infty)$ where the function is not differentiable are zero.