find the value of a so that the function f(x)=xe^ax has a critical point at x=6 ?
A critical point, or stationary point, is where the slope of the curve (i.e. its derivative) is zero.
y = x.e^(ax)
y' = e^(ax) + ax.e^(ax)
y' = e^(ax)(1 + ax)
set y' = 0, at x = 6, giving
a = -1/6
So the function y = x.e^(-x/6) has a zero slope at x = 6, i.e when a = -1/6