The function $\mathrm{f}(x)=x^3-6 x^2+9 x+2$ has maximum value when $x$ is

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Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{f}(x)=x^3-6 x^2+9 x+2 \ 	herefore \quad & \mathrm{f}^{\prime}(x)=3 x^2-12 x+9 \end{aligned}$ For maximum or minimum, $\begin{aligned} & \mathrm{f}^{\prime}(x)=0 \ & \Rightarrow 3 x^2-12 x+9=0 \ & \Rightarrow 3(x-1)(x-3)=0 \ & \Rightarrow x=1,3 \end{aligned}$ Now, $\mathrm{f}^{\prime \prime}(x)=6 x-12$ $	herefore \quad \mathrm{f}^{\prime \prime}(1)=-6 < 0$ $	herefore \quad \mathrm{f}(x)$ is maximum at $x=1$.

The function $\mathrm{f}(x)=x^3-6 x^2+9 x+2$ has maximum value when $x$ is

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