Function $$f(x)=e^{-1 / x}$$ is strictly increasing for all $$x$$ where

If $$x=-2$$ and $$x=4$$ are the extreme points of $$y=x^3-\alpha x^2-\beta x+5$$, then

10 is divided into two parts such that the sum of double of the first and square of the other is minimum, then the numbers are respectively

The function $$f(x)=\frac{\lambda \sin x+6 \cos x}{2 \sin x+3 \cos x}$$ is increasing, if