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Calculus I.S.I. and C.M.I. Entrance ISI Entrance Videos

Derivative of Function | TOMATO BStat Objective 767

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on a derivative of Function. You may use sequential hints to solve the problem.

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

Derivative of Function and absolute value (B.Stat Objective Question )


Let \(f(x)=|sin^{3}x|\), \(g(x)=sin^{3}x\), both being defined for x in the interval \((\frac{-\pi}{2}, \frac{\pi}{2})\). Then

  • \(f'(x)=g'(x) for all x\)
  • \(g'(x)=|f'(x)| for all x\)
  • \(f'(x)=|g'(x)| for all x\)
  • \(f'(x)=-g'(x) for all x\)

Key Concepts


Equation

Derivative

Algebra

Check the Answer


But try the problem first…

Answer:\(g'(x)=|f'(x)| for all x\)

Source
Suggested Reading

B.Stat Objective Problem 767

Challenges and Thrills of Pre-College Mathematics by University Press

Try with Hints


First hint

Let \(f(x) =|sin^{3}x|=sin^{2}x|sinx|\)

\(f'(x)=2cos(x)sin(x)|sin(x)|+\frac{cos(x)(sin^{3}x)}{|sin(x)|}\)

=\(3sin(x)cos(x)|sin(x)|\)

Second Hint

or, \(g(x)=sin^{3}x\)

or, \(g'(x)=3 cosx sin^{2}x\)

Final Step

or, |f'(x)| for all \(x \in (\frac{-\pi}{2},\frac{\pi}{2})\) = \(3cos x|sin x||sin x|=g'(x)\)

or, |f'(x)|=g'(x) for all \(x \in (\frac{-\pi}{2},\frac{\pi}{2})\)

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