Calculus
posted by Bud .
For the function g(x) = xe power x, there is inflection point at?

g(x) = xe^x
g'(x) = xe^x + e^x
g''(x) = xe^x + e^x + e^x
= e^x( x+2)
at point of inflection g''(x) = 0
so e^x = 0 > no solution
or x+2 = 0
x = 2
then g(2) = 2e^2 or 2/e^2
point of inflection (2, 2/e^2) 
The average value of f(x) = e ^ 4xsquared on the interval [1/4,1/4]