JEE Exam  >  JEE Questions  >   The function f(x) = x3 - 3x is ....... .a)in... Start Learning for Free
The function f(x) = x3 - 3x is ....... .
  • a)
    increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)
  • b)
    increasing in (0, ∞) and decreasing in (-∞, 0)
  • c)
    decreasing in(0, ∞) and increasing in (-∞, 0)
  • d)
    decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ...
We have, function f(x) = x3 - 3x
⇒f’(x) = 3x2 - 3 = 3(x + 1)(x - 1)
f’(x) = 0 ⇒ x = -1,1
Hence, f'(x) > 0 in (-∞, -1) ∪ (1, ∞) and f'(x) < o="" in="" (-1,="" />
∴ f(x) is increasing in (-∞, -1), ∪(1, ∞) and decreasing in (-1, 1).
This question is part of UPSC exam. View all JEE courses
Most Upvoted Answer
The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ...
Explanation:

Increasing and Decreasing Intervals:
- To determine where the function is increasing or decreasing, we need to find the critical points of the function.
- The critical points occur where the derivative of the function is equal to zero or undefined.
- Taking the derivative of f(x) = x^3 - 3x, we get f'(x) = 3x^2 - 3.
- Setting f'(x) = 0, we find the critical points at x = -1 and x = 1.
- Now, we can test the intervals between these critical points to determine where the function is increasing or decreasing.

Interval Analysis:
- For x < -1,="" choose="" x="-2." substituting="" x="-2" into="" f'(x),="" we="" get="" f'(-2)="3(-2)^2" -="" 3="9" -="" 3="6." this="" means="" f(x)="" is="" increasing="" in="" (-∞,="" />
- For -1 < x="" />< 1,="" choose="" x="0." substituting="" x="0" into="" f'(x),="" we="" get="" f'(0)="3(0)^2" -="" 3="-3." this="" means="" f(x)="" is="" decreasing="" in="" (-1,="" />
- For x > 1, choose x = 2. Substituting x = 2 into f'(x), we get f'(2) = 3(2)^2 - 3 = 9 - 3 = 6. This means f(x) is increasing in (1, ∞).
Therefore, the function f(x) = x^3 - 3x is increasing in (-∞, -1) ∪ (1, ∞) and decreasing in (-1, 1), which matches with option 'A'.
Explore Courses for JEE exam
The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer?
Question Description
The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer?.
Solutions for The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice The function f(x) = x3 - 3x is ....... .a)increasing in ( -∞, - 1) ∪ ( 1, ∞) and decreasing in (-1, 1)b)increasing in (0, ∞) and decreasing in (-∞, 0)c)decreasing in(0, ∞) and increasing in (-∞, 0)d)decreasing in (-∞, -1) ∪ (1, ∞)and increasing in (-1, 1)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice JEE tests.
Explore Courses for JEE exam

Top Courses for JEE

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev