find the value of a so that the function f(x)=xe^ax has a critical point at x=6

Question

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Answer 1

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