Let $\displaystyle {f{{\left({x}\right)}}}$ be a continuous function defined on the interval $\displaystyle {2}\le{x}\lt\infty$ such that
$\displaystyle {f{{\left({2}\right)}}}={15}$

$\displaystyle {\left|{f{{\left({x}\right)}}}\right|}<{x}^{{{7}}}+{11}$
and
$\displaystyle {\int_{{{2}}}^{{\infty}}}{f{{\left({x}\right)}}}{e}^{{-\frac{{x}}{{4}}}},{\left.{d}{x}\right.}=-{2}$

Determine the value of
$\displaystyle {\int_{{{2}}}^{{\infty}}}{f}'{\left({x}\right)}{e}^{{-\frac{{x}}{{4}}}},{\left.{d}{x}\right.}$
Preview Question 6