SOLUTION: Find the x-coordinates of the inflections points of the function f(x) = x^4 - 8x^3 + 18x^2 - 3

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Question 1026207: Find the x-coordinates of the inflections points of the function f(x) = x^4 - 8x^3 + 18x^2 - 3
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
y+=++x%5E4+-+8x%5E3+%2B+18x%5E2+-+3 ==> y' = 4x%5E3-24x%5E2%2B36x ==> y" = 12x%5E2+-48x+%2B+36 (Verify!!)
Inflection points are where the sign of the concavity of the curve changes, which is described by the 2nd derivative y".
Set y" = 0.
==> y" = 12x%5E2+-48x+%2B+36+=+0 ==> x = 1, 3.
Between negative infinity to 1, y" > 0.
Between 1 and 3, y" < 0.
Between 3 and positive infinity, y" > 0.
Thus points of inflection exist at x = 1 and x = 3.