The minimum value of $f (x) = e^{(x^{4} - x^{3} + x^{2})}$ is

e

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1

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Solution

The correct option is D $1$
$f (x) = e^{(x^{4} - x^{3} + x^{2})}, f^{'} (x) = e^{x^{4} - x^{3} + x^{2}}$
$(4 x^{3} - 3 x^{2} + 2 x)$
$\Rightarrow f (x)$ is decreasing for $x < 0$ , increasing for $x > 0$ .
Minimum is at $x = 0$
Hence, minimum value of $f (x) = f (0) = e^{0} = 1$

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