Question

find any critical numbers of the function. (Enter your answers as a comma-separated list.)

g(x) = x5 − 10x3

Answer 1

You'll have to determine 1st derivative to find critical points:
g'(x)=5x^4 - 30x^2
Set g'(x)=0
5x^4 - 30x^2=0
x^4 - 6x^2 = 0
x^2(x^2 - 6) = 0
x^2 = 0
x1=x2=0
x^2 - 6 = 0
x^2 = 6
x3=+sqrt6
x4=-sqrt6
The critical points are the roots of derivative: -sqrt6,0,sqrt6