Let f(x)=xeax;               x≤0x+ax2−x3;    x>0   where a ' is a positive constant. Find  the interval in which f′(x) is increasing.

f′(x)=eax+axeax ;x≤01+2ax−3x2;x>0f′′(x)=2aeax+a2xeax;x≤02a−6x;x>0 For f′(x) to be an increasing function f′′(x)≥0 i.e.,  aeax(2+ax)≥0⇒x≥−2a2a−6x≥0⇒x≤a3∴ The int erval inwhich f′(x) is increasing is −2a,a3