Question

For the function g(x) = xe power x, there is inflection point at?

Answer 1

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)

Answer 2

The average value of f(x) = e ^ 4xsquared on the interval [-1/4,1/4]