Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative of Function.
Consider the function \(f(x)=|sin(x)|+|cos(x)|\) defined for x in the interval \((0,{2\pi})\)
Equation
Derivative
Algebra
Answer:f(x) is not differentiable at x=\(\frac{\pi}{2}\), \({\pi}\) and \(\frac{3\pi}{2}\) and differentiable everywhere else.
B.Stat Objective Problem 759
Challenges and Thrills of Pre-College Mathematics by University Press
\(f(x)=|sin(x)|+|cos(x)|\)
or, \(f'(x)=\frac{sinxcosx}{|sinx|} - \frac{cosxsinx}{|cosx|}\)
f(x) is not differentiable at x=\(\frac{\pi}{2}\), \({\pi}\) and \(\frac{3\pi}{2}\) and differentiable everywhere else.
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