Let $f$ be a continuous function defined on the interval $[2, \infty[$ such that $f(4)=14$, $|f(x)| < x^3+10$, and $$\int_4^\infty f(x)e^{-x/4} dx=-5\;.$$
Determine the value of: $$\int_4^\infty f\,'(x)e^{-x/4} dx\;.$$
Let $f$ be a continuous function defined on the interval $[2, \infty[$ such that $f(4)=14$, $|f(x)| < x^3+10$, and $$\int_4^\infty f(x)e^{-x/4} dx=-5\;.$$
Determine the value of: $$\int_4^\infty f\,'(x)e^{-x/4} dx\;.$$