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The minimum value of $f(x)=e^{\left(x^4-x^3+x^2\right)}$ is
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Hints: $f(x)=e^{\left(x^4-x^3+x^2\right)}, f^{\prime}(x)=e^{x^4-x^3+x^2}$
$e^{x^4-x^3+x^2}\left(4 x^3-3 x^2+2 x\right) x\left(4 x^2-3 x+2\right)$
$\Rightarrow f(x)$ is decreasing for $x < 0$, increasing for $x>0$
$\therefore$ Minimum is at $\mathrm{x}=0 \quad \therefore \mathrm{f}(0)=\mathrm{e}^0=1$
$e^{x^4-x^3+x^2}\left(4 x^3-3 x^2+2 x\right) x\left(4 x^2-3 x+2\right)$
$\Rightarrow f(x)$ is decreasing for $x < 0$, increasing for $x>0$
$\therefore$ Minimum is at $\mathrm{x}=0 \quad \therefore \mathrm{f}(0)=\mathrm{e}^0=1$
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