What are the x values where inflection may occur in f(x)=x^4-6x^3+5x?

Question

Can you show me how its done. This is a calculus problem.Thank you.

Answer 1

f´(x)= 4x^3-18x^2+5

f´´(x) = 12x^2-36x ( 2nd derivative
f´´(x)=0
x(12x-36)= 0
so x=0 and x=3 are the points.
As f´´(x) changes it sign at x=0 an x=3 These are real points of inflection

Answer 2

f ' = 4x^3 -18x^2 +5
f '' = 12x^2 -36x
at inflection f ''= 0
so
x^2 - 3x =0 simplified
x = 0 , 3
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