Polynomial/Continuity/Check delta/1/Exercise

Let

${}f(x)=2x^{3}-4x+5\,.$

Show that for all ${}x\in \mathbb {R}$, the following relation holds: If

${}\vert {x-3}\vert \leq {\frac {1}{800}}\,,$

then

${}\vert {f(x)-f(3)}\vert \leq {\frac {1}{10}}\,.$

Create a solution