Explanation

(c)
Given, $f(x) = \int_{- 10}^{x}{\left( t^{4} - 4 \right)e^{- 4t}}\ dt$
On differentiating w.r.t. $x$, we get
$f^{'}(x) = \left( x^{4} - 4 \right)e^{- 4x}$
For maxima or minima, put $f^{'}(x) = 0$
$\Rightarrow \ \ x = \pm \sqrt{2},\ \pm \sqrt{2}$
Again on differentiating w.r.t. $x$, we get
$f^{''}(x) = - 4\left( x^{4} - 4 \right)e^{- 4x} + 4x^{3\ ^{\ }}e^{- 4x}$
At $x = \sqrt{2}$ and $x = - \sqrt{2}$, the given function has two extreme values