Question

Determine the x-value for each inflection point on the graph of the following function.
f(x)=3x^5-5x^4-80x^3+360x^2+1000x+850

Answer 1

inflection at y'' = 0

y' = 15x^4 - 20x^3 - 240x^2 + 720x + 1000

y'' = 60x^3 - 60x^2 - 480x + 720

so solve y'' = 0

x^3 - x^2 - 8x + 12 = 0

(x-2)(x-2)(x+3) = 0

There you have the x values. I trust you can evaluate y(x) to get the rest.

Answer 2

so would the inflection point be x=-3 because that's where it goes from decreasing to increasing

Answer 3

yes