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 $|f(q)|\le \frac{1}{10}$.

Create a solution