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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 \((0,{2\pi})\)

- f(x) is differentiable everywhere
- f(x) is not differentiable at x=\(\frac{\pi}{2}\), \({\pi}\) and \(\frac{3\pi}{2}\) and differentiable everywhere else.
- f(x) is not differentiable at x=\(\frac{\pi}{2}\) and \(\frac{3\pi}{2}\) and differentiable everywhere else
- none of the foregoing statements is true.

Equation

Derivative

Algebra

But try the problem first...

Answer:f(x) is not differentiable at x=\(\frac{\pi}{2}\), \({\pi}\) and \(\frac{3\pi}{2}\) and differentiable everywhere else.

Source

Suggested Reading

B.Stat Objective Problem 759

Challenges and Thrills of Pre-College Mathematics by University Press

First hint

\(f(x)=|sin(x)|+|cos(x)|\)

or, \(f'(x)=\frac{sinxcosx}{|sinx|} - \frac{cosxsinx}{|cosx|}\)

Second Hint

Final Step

f(x) is not differentiable at x=\(\frac{\pi}{2}\), \({\pi}\) and \(\frac{3\pi}{2}\) and differentiable everywhere else.

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