Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals:  f (x) = sin x + cos x , x [0, p]

5 Find the absolute maximum value and the absolute minimum value of the following
functions in the given intervals:

(ii) f (x) = \sin x + \cos x , x \epsilon [0, \pi]

Answers (1)

best_answer

Given function is 
f(x) = \sin x + \cos x
f^{'}(x) = \cos x - \sin x\\ f^{'}(x)= 0\\ \cos x- \sin x= 0\\ \cos = \sin x\\ x = \frac{\pi}{4}         as    x \ \epsilon \ [0,\pi]
Hence, x = \frac{\pi}{4} is the critical point  of the function f(x) = \sin x + \cos x
Now, we need to check the value of function f(x) = \sin x + \cos x  at x = \frac{\pi}{4}  and at the end points of given range  i.e. x = 0 \ and \ x = \pi
f(\frac{\pi}{4}) = \sin \frac{\pi}{4} + \cos \frac{\pi}{4}\\
            =\frac{1}{\sqrt2}+\frac{1}{\sqrt2} = \frac{2}{\sqrt2} = \sqrt2
f(0) = \sin 0 + \cos 0 = 0 + 1 = 1
f(\pi) = \sin \pi + \cos \pi = 0 +(-1) = -1
Hence, the absolute maximum value of function f(x) = \sin x + \cos x occurs at x = \frac{\pi}{4} and value is \sqrt2
and absolute minimum value of function f(x) = \sin x + \cos x occurs at x = \pi and value is -1

Posted by

Gautam harsolia

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Date Sheet 2025 (Out) Live: Class 10, 12 board exam time table at cbse.gov.in; syllabus, sample papers
anam-khan

CBSE Class 12 board exam date sheet 2025 out; exams from February 15 to April 4
anam-khan

When will CBSE Board exam 2025 date sheet be released for Class 10, 12?

Latest Question