How do you find the inflection points for the given function f(x)=x^3-3x^2+6x?

Lexi Holmes

Lexi Holmes

Answered question

2023-03-25

How to find the inflection points for the given function f ( x ) = x 3 - 3 x 2 + 6 x ?

Answer & Explanation

unnlattpdui

unnlattpdui

Beginner2023-03-26Added 5 answers

f ( x ) = x 3 - 3 x 2 + 6 x
f ( x ) = 3 x 2 - 6 x + 6
f ( x ) = 6 x - 6
When the second derivative equals zero, inflexion points can be found.
For inflexion points, f ( x ) = 0
6 x - 6 = 0
x = 1
Test x = 1 for concavity
When x = 0 , f ( 0 ) = - 6
When x = 1 , f ( 1 ) = 0
When x = 2 , f ( 2 ) = 6
Hence, since there is a change in concavity, there is a point of inflexion at (1,4)

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