Given the following non$-$linear expression $f(x)=e^{-x}-3x^2+2$

Problem $1$:

Using MATLAB, approximate the root of $f(x)$ via a graphing technique.

Problem $2$:

Perform $5$ iterations of the bisection method with $\left[\begin{array}{cc}-5& 5\end{array}\right]$ as the initial bracket to find the root of $f(x).$ Show your

handwritten calculations and tabulate your results.

Problem $3$:

Using MATLAB, perform $100$ iterations of the bisection method using the same initial bracket and $f(x)$ as before.

Use format long and plot the estimated relative error VS iteration number.