`Let f(x)=`{`x e^(a x),x lt=0;x+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 a is a positive constant . The interval in which f '(x) is increasing is [(k)/(a ),(a)/(l)], Then k +l is equal to ______

Let f(x)=(3x-7)x^(2/3) . The interval in which f(x) is increasing.

Find the intervals in which f(x)=x/2+2/x , x!=0 is increasing or decreasing.

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

Find the intervals in which f(x)=8+36 x+3x^2-2x^3 is increasing or decreasing.

Find the intervals in which f(x)=6+12 x+3x^2-2x^3 is increasing or decreasing.

Find the intervals in which f(x)=x/2+2/x ,\ \ x!=0 is increasing or decreasing.

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}