Question

inflection point of g(x)=xe^-2x

Answer 1

take the derisive

then set the derivative equal to zero, the numbers you get from this tell you where the function changes

then sub numbers into the derivative on either side of where the function changes,

if

f'(x) > 0 then the function is increasing
if
f'(x) < 0 then the function is decreasing

Answer 2

an inflection point is an area where on both sides of the critical number, the function is increasing, and then increasing on the other interval
or
an inflection point is an area where on both sides of the critical number, the function is decreasing, and then decreasing on the other interval

Make a Chart like this



in this case the function has a min, as it is increasing on one interval then decreasing on the one after it