The function f(x) = |cos x| is | vedclass

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(B) The given function is $f(x) = |\cos x|$.We know that the function $g(x) = \cos x$ is continuous and differentiable for all $x \in R$.The modulus f

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Everywhere continuous but not differentiable at odd multiples of $\pi / 2$

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(B) The given function is $f(x) = |\cos x|$.We know that the function $g(x) = \cos x$ is continuous and differentiable for all $x \in R$.The modulus function $h(x) = |x|$ is continuous everywhere but not differentiable at $x = 0$.Therefore,the composite function $f(x) = |\cos x|$ is continuous for all $x \in R$.However,$f(x)$ will not be differentiable where the expression inside the modulus is zero,i.e.,at $\cos x = 0$.This occurs at $x = (2n + 1) \frac{\pi}{2}$ for all $n \in Z$.At these points,the graph of $f(x)$ has sharp corners (cusps),as shown in the graph.Thus,$f(x)$ is everywhere continuous but not differentiable at odd multiples of $\frac{\pi}{2}$.

The function $f(x) = |\cos x|$ is

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