Find the local maxima and local minima, if any , of the following function.Also, find the local maximun and local minimum values as the case maybe:

f(x)=\sin x+\frac{1}{2}\cos 2x, 0\leq x\leq \frac{\pi}{2}

 

 

 

 
 
 
 
 

Answers (1)

f(x)=\sin x+\frac{1}{2}\cos x, 0\leq x\leq \frac{\pi}{2}

f'(x)=\cos x - \sin 2x =0

\cos x =\sin 2x

\cos x =2\sin x\cdot \cos x

1 =2\sin x

\sin x=1/2 .........(1)

Differentiating again,

f''(x)=- \sin x-2\cos 2x

=-1/2-1=-3/2< 0

x=\frac{\pi}{6}\Rightarrow local\: maxima

f\left ( \frac{\pi}{6} \right )= \sin \frac{x}{6}+\frac{1}{2}\cos 2 \times \frac{\pi}{6}

=\frac{1}{2}+\frac{1}{2}.\frac{1}{2}

=\frac{3}{4}  ...........Local Maxima.

 

Preparation Products

Knockout KCET 2021

An exhaustive E-learning program for the complete preparation of KCET exam..

₹ 4999/- ₹ 2999/-
Buy Now
Knockout KCET JEE Main 2021

It is an exhaustive preparation module made exclusively for cracking JEE & KCET.

₹ 27999/- ₹ 16999/-
Buy Now
Knockout NEET Sept 2020

An exhaustive E-learning program for the complete preparation of NEET..

₹ 15999/- ₹ 6999/-
Buy Now
Rank Booster NEET 2020

This course will help student to be better prepared and study in the right direction for NEET..

₹ 9999/- ₹ 4999/-
Buy Now
Knockout JEE Main Sept 2020

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 12999/- ₹ 6999/-
Buy Now
Exams
Articles
Questions