Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: g(x) = x ^ 3 – 3x

3. Find the local maxima and local minima, if any, of the following functions. Find
also the local maximum and the local minimum values, as the case may be:
 (ii) g(x) = x ^3 - 3x

Answers (1)

best_answer

Given function is 
g(x) = x ^3 - 3x\\ g^{'}(x) = 3x^2 - 3\\ g^{'}(x)=0\Rightarrow 3x^2-3 =0 \Rightarrow x = \pm 1\\
Hence, the critical points are 1 and - 1
Now, by second derivative test 
g^{''}(x)=6x
g^{''}(1)=6 > 0
Hence, 1 is the point of minima and the minimum value is 
g(1) = (1)^3 - 3(1) = 1 - 3 = -2
g^{''}(-1)=-6 < 0
Hence, -1 is the point of maxima and the maximum value is 
g(1) = (-1)^3 - 3(-1) = -1 + 3 = 2

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 Class 10, 12 practical exams 2025 for compartment students from July 10; detailed guidelines issued
anam-khan

CBSE Central Sector Scheme of Scholarship 2025 applications open on scholarships.gov.in
anam-khan

CBSE Board 2025: Class 10th, 12th supplementary date sheet out; exams from July 15

Latest Question