Given y = x^4 − 4x^2 + 50. Find any extrema and any points of inflection

Answer 1

f' = 4 x^3 -8 x = 4x (x^2-2)
zero at x = 0 and x = sqrt 2 and x=-sqrt 2

f" = 12 x^2 - 8

at zero this is -8 so a maximum

at +sqrt 2 this is +16
same at -sqrt2 so those are minima

Huge positive for x large positive and for x large negative