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Q.
If $f:[2,3] \rightarrow R$ is defined by $f(x)=x^{3}+3 x-2$, then the range of $f(x)$ is contained in the interval
NTA AbhyasNTA Abhyas 2022Relations and Functions - Part 2
Solution:
Given, $f(x)=x^{3}+3 x-2$
On differentiating w.r.t. $x$, we get
$f^{\prime}(x)=3 x^{2}+3>0 \forall x \in R$
$\therefore f(x)$ is increasing
At $x=2, f(2)=2^{3}+3(2)-2=12$
At $x=3, f(3)=3^{3}+3(3)-2=34$
$\therefore f(x) \in[12,34]$