Exponential function/Cubic Taylor-approximation/Zero/Exercise

We consider the polynomial

${}P=1+X+{\frac {1}{2}}X^{2}+{\frac {1}{6}}X^{3}\,.$

1. Compute the value of ${}P$ for the points ${}-2,-1,0,1,2$.
2. Sketch the graph of ${}P$ on the interval ${}[-2,2]$. Does there exist a relation to the exponential function ${}e^{x}$?
3. Determine a zero of ${}P$ within ${}[-2,2]$, with an error of at most ${}{\frac {1}{4}}$.

Create a solution