Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Derivative of Function.

Derivative of Function Problem (B.Stat Objective Question )


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.

Key Concepts


Equation

Derivative

Algebra

Check the Answer


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

Try with Hints


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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