Find the interval(s) where the function is increasing and the interval(s) where it is decreasing. (Enter your answers using interval notation. If an answer does not exist, enter DNE.)

Question

g(x) = x⁴ − 18x² + 1

Answer 1

g(x)= x^4-18x^2+1 is increasing when g'(x)>0, decreasing when g'(x)<0, neither when g'(x)=0

g'(x)=4x^3-36x =0

4x(x^2-9)=0

x^2=9

x=-3 or 3 or 0 are values of x where f(x) changes from increasing to decreasing or from decreasing to increasing

(-infinity,-3)U(0,3) has decreasing f(x)

(-3,0)U(3,infinity) has increasing f(x)