The range of values of $x$ for which $f(x)=x^3+6 x^2-36 x+7$ is increasing in

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Aicharya · Accepted Answer

$\begin{aligned} \mathrm{f}(x) & =x^3+6 x^2-36 x+7 \ \mathrm{f}^{\prime}(x) & =3 x^2+12 x-36 \ & =3\left(x^2+4 x-12ight) \end{aligned}$ For $\mathrm{f}(x)$ to be increasing, $\begin{aligned} & \mathrm{f}^{\prime}(x)>0 \ & \Rightarrow 3\left(x^2+4 x-12ight)>0 \ & \Rightarrow x^2+4 x-12>0 \ & \Rightarrow(x+6)(x-2)>0 \ & \Rightarrow x \in(-\infty,-6) \cup(2, \infty) \end{aligned}$

The range of values of $x$ for which $f(x)=x^3+6 x^2-36 x+7$ is increasing in

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