`L e tf(x)={x e^(a x),xlt=0x+a x^2-x^3,x >0` where `a` is a positive constant. Find the interval in which `f^(prime)(x)` is increasing.

Let f(x)={{:(xe^(ax)",", x le0),(x+ax^2-x^3",",x gt 0):} where a is postive constant . Find the interval in which f'(X) is increasing.

Find the interval in which f(x)=2x^(3)+3x^(2)-12x+1 is increasing.

Let f(x)={{:(xe^(ax) "," x le 0 ),(x+ax^2-x^3 "," x gt 0 ):} ,where is a positive constant .Then the interval in which f' (x ) is increasing is

Let f (x)= {{:( xe ^(ax)"," , x le 0),( x+ ax ^(2)-x ^(3)"," , x gt 0):} Where a is a positive constnat . The interval in which f '(x) is increasing is [(k)/(a ),(a)/(l)], Then k +l is equal to

f(x)=cos((pi)/(x)), x ne 0 , find the interval in which f(x) in increasing.

Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreasing.

Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreasing.

If f(x)=|x|e^(x), then at x=0

The interval in which the function f(x)=x^(e^(2-x)) increases is

Find the intervals in which f(x)=5+36x+3x^(2)-2x^(3) is increasing or decreasing.