Motivation: In this question we use the Newton method and, the Matlab function fzero function. In lectures $($Lecture $07)$ we have seen that these methods can for instance be used to find the implied volatility of financial assets.

The goal is to approximate the value $0<$ z$*<2$ for which the function

f$($z$)=$ e$^$z $-2*$z$^2(1)$

satisfies f$($z$")=0.$

i$)$ Compute f given by $(1)$ and its derivative f$\text{'}(2)=$ e$^$z $-4$z at the points zi $=$ i$/10$ for i $=0,1,2,...,20.$ Store the results in the row vectors fz and dfz$,$ respectively.