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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

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

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.