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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

Question 592216: find the least integral upper bound of the zeros of the function f%28x%29=x%5E3-x%5E2%2B1
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) About Me  (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.