Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

Find the intervals on which $f$ is increasing or decreasing. $f(x)= x^{3}-3x+1$

Note: This is part 2nd of a 6 part question, split as 6 separate questions here.

Can you answer this question?

1 Answer

0 votes
  • (i) If $f'$ is positive on an open interval $I$. Then $f$ is strictly increasing on $I$
  • (ii) If $f'$ is negative on an open interval $I$, then $f$ is strictly decreasing on $I$
Step 1:
$f'(x)=0\;when \;x=-1,1$
Step 2:
Interval $-\infty < x < -1$
$(x+1)\;= -$
$f'c (x)\;=+$
Interval of inc /dec $f(x)$= $f(x)$ is increasing in $(-\infty,-1]$
Interval $-1 < x<1$
$(x+1)\;= +$
$f'c (x)\;=-$
Interval of inc /dec $f(x)$= $f(x)$ is decreasing in $[1,-1]$
Interval $1 < x <\infty$
$(x+1)\;= +$
$f'c (x)\;=+$
Interval of inc /dec $f(x)$= $f(x)$ is increasing in $[1,\infty]$
$\therefore \;f(x)$ increasing in $(- \infty,-1] \cup [1, \infty)$ and decreasing in $[-1,1]$
answered Jul 30, 2013 by meena.p

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App