Question

use the intermediate value theorem to find intervals one unit in length in which the polynomial function is guranteed to have a zero.
f(x)=x^3-3x^2+3

Answer 1

make a nice guess for where this is near zero, i.e. find two successive integers for which \(f\) is negative and \(f\) is positive

Answer 2

-1 and 0 would work
also 1 and 2

Answer 3

\(f(-1)=-1-3+3=-1\) and \(f(0)=3\) so first \(f\) in negative, then positive, so it must be zero some where in between

Answer 4

how about h(x)=x^4-10x^2+3