Answer:
[tex]x\in (-2,0)\cup (2,\infty)[/tex]
Step-by-step explanation:
Find the derivative of the function [tex]y=x^4 -8x^2 +16:[/tex]
[tex]y'=4x^3 -8\cdot 2x\\ \\y'=4x^3 -16x[/tex]
The function is increasing when [tex]y'>0,[/tex] so solve the inequality
[tex]4x^3-16x>0\\ \\4x(x^2-4)>0\\ \\4x(x-2)(x+2)>0\\ \\x\in (-2,0)\cup (2,\infty)[/tex]
You can see from the graph that the function increases for [tex]x\in (-2,0)\cup (2,\infty)[/tex]
