Question

how to find the stationary point of the curve when y=xe^-2x

Answer 1

sorry i had to repost the question because my earlier question was stated wrong :D

Answer 2

Derivative e^-2x(1-2x) -> x= 1/2 for max

Answer 3

i found out that derivative is -2e^-2x is that right? if so where do i go from here to get x=1/2

Answer 4

i found this
(x x)/e^2 = 0 at x = 0

Answer 5

and thats for minimum btw

Answer 6

The derivative is what I said, which gives you the half.

Answer 7

I think its important to know Stationary points of a curve ar the points where, for example, if you move from left to right,the curve is increasing, reaches a maximum point, stops, and then starts decreasing, the very top point (the maximum) is the stationary point, there can also be the minimimum point (if the curve is like a valley).
this equates to a slope of zero, hence, reason for finding derivative here, which gives you slope.

Answer 8

You can find the concavity with a second derivative (derivative of the derivative).