Polynomial/x^3+x-1/Zero between 0 and 1/Computation/Exercise

Consider

$f(x)=x^{3}+x-1.$

a) Prove that the function ${}f$ has in the real interval ${}[0,1]$ exactly one zero.

b) Compute the first decimal digit in the decimal system of this zero point.

c) Find a rational number ${}q\in [0,1]$ such that ${}\vert {f(q)}\vert \leq {\frac {1}{10}}$.

Create a solution