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.

 

Most Viewed Questions

Related Chapters

Preparation Products

Knockout CUET (Physics, Chemistry and Mathematics)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout CUET (Physics, Chemistry and Biology)

Complete Study Material based on Class 12th Syllabus, 10000+ Question Bank, Unlimited Chapter-Wise and Subject-Wise Mock Tests, Study Improvement Plan.

₹ 7999/- ₹ 4999/-
Buy Now
Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
Buy Now
Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions