Explanation

(c)
$x^{4} - x^{3} + x^{2} = x^{2}\left( x^{2} - x + 1 \right)$
$\ = x^{2}\left\lbrack \left( x - \frac{1}{2} \right)^{2} + \frac{3}{4} \right\rbrack$
$\therefore\ \ \ f(x) = e^{x^{4} - x^{3} + x^{2}}will\ attain\ minimum$
At $x = 0$
$\Rightarrow \ Minimum\ of\ f(x) = 1$