Question

f(x) = x^4 - 40 x^3 At what value(s) of x does f have a local maximum or a local minimum? Find the x-coordinates of all inflection points

Answer 1

I found the values of x that slope of the curve = 0 (0,30)

Answer 2

just cant find the max and the min

Answer 3

and the x-coordinates of all inflection points

Answer 4

Calculus or algebra?

Answer 5

calculus

Answer 6

First derivative, 4x^3-120x^2=0=4x^2(x-30), x=0,30. Plug x points into original to find if max or min.

Second derivative, 12x^2-240x=0=12x(x-20), x=0,20. Plug x points into first derivative to find inflection.

Answer 7

i dont know if this right but I got (0,702,000) and (0,-16,000)