INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

May 19, 2020

Derivative of Function | TOMATO BStat Objective 767

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


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

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 \(x \in (\frac{-\pi}{2},\frac{\pi}{2})\)

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
enter