SOLUTION: find the least integral upper bound of the zeros of the function {{{f(x)=x^3-x^2+1}}} Can you please show me step by step how to do this problem? My textbook did not explain it cl

Question 592216: find the least integral upper bound of the zeros of the function
Can you please show me step by step how to do this problem? My textbook did not explain it clearly at all, and as I use a correspondance course, I do not have a teacher I can ask for help. Any help you can give will be greatly appreciated, and if you can show me the concept clearly so that I can understand not only this problem but others like it, I would be so very grateful. Thank you and God bless you for your time!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We know that

f(-1) = -1
f(0) = 1
f(1) = 1
f(2) = 5
f(3) = 19

And f continually increases after x > 3 (more or less) because its derivative is positive when x > 3.

Since f is continuous everywhere, and the sign of f changes from - to + between -1 and 0, we conclude that there must be a zero in the interval -1 < x < 0. Therefore 0 is the least integral upper bound.
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