Browse by Stream
QnA
Home
Search for Exam, Articles, Questions
QnA
get app
Go To Your Study Dashboard
  1. Home
  2. 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
# NCERT

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)
G Gautam harsolia

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

Similar Questions

Related Chapters

Preparation Products

Knockout NEET May 2021 (One Month)

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

₹ 14000/- ₹ 6999/-
Buy Now
Foundation 2021 Class 10th Maths

Master Maths with "Foundation course for class 10th" -AI Enabled Personalized Coaching -200+ Video lectures -Chapter-wise tests.

₹ 350/- ₹ 112/-
Buy Now
Knockout JEE Main April 2021 (One Month)

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

₹ 14000/- ₹ 6999/-
Buy Now
Knockout NEET May 2021

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

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2021

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

₹ 22999/- ₹ 14999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
Start Now
 
Exams
Articles
Questions