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

Note: This is part 3rd of a 6 part question, split as 6 separate questions here.

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  • (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 $I$
$f(x)= x^3+x+1$
$f'(x)=3x^2+1 > 0$ for all $ x \in R$
$\therefore f(x)$ is a strictly increasing function on $R$
answered Jul 30, 2013 by meena.p
 

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