SOLUTION: Find the minimum of function f(x) = (x+1)^3 - (x-1)^3

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Question 388286: Find the minimum of function f(x) = (x+1)^3 - (x-1)^3

Found 2 solutions by Fombitz, Alan3354:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Simplify,
f%28x%29=x%5E3%2B3x%5E2%2B3x%2B1-x%5E3%2B3x%5E2-3x%2B1=6x%5E2%2B2
In vertex form, that would be,
f%28x%29=6%28x-0%29%5E2%2B2
with a minimum value of,
highlight%28y%5Bmin%5D=2%29

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the minimum of function f(x) = (x+1)^3 - (x-1)^3
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f'(x) = 3(x+1)^2 - 3(x-1)^2
3(x+1)^2 - 3(x-1)^2 = 0
(x+1)^2 - (x-1)^2 = 0
x%5E2+%2B+2x+%2B+1+-+x%5E2+%2B+2x+-+1+=+0
4x = 0
Min at x = 0
f(0) = 2
Minimum at (0,2)