SOLUTION: If -1<=x<=1 then what is the maximum possible value of x^3-x^2-x=1? Thanks

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Question 329550: If -1<=x<=1 then what is the maximum possible value of x^3-x^2-x=1?
Thanks
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
graph%28300%2C300%2C-1%2C1%2C-2%2C1%2Cx%5E3-x%5E2-x-1%29
f%28x%29=x%5E3-x%5E2-x-1
df%2Fdx=3x%5E2-2x-1=0
%283x%2B1%29%28x-1%29=0
Two solutions:
x-1=0
x=1
.
.
.
3x%2B1=0
3x=-1
x=-1%2F3
The max. value occurs at x=-1%2F3.
f%28-1%2F3%29=-1%2F27-1%2F9%2B1%2F3-1
f%28-1%2F3%29=-22%2F27