What’s the local max/min of: y = 3x^5 - 10x^3 + 45x

Question

I know that it’s only supposed to be increasing, but since there’s a change in concavity, does there have to be a local max/min value?

Answer 1

y' = 15x⁴ - 30x² + 45 = 15(x⁴ - 2x² + 3) = 15(x² - 1)² + 30 > 0 for all real x. So, this function increasing and no local extrema.