Additional problem $3$: Write a function lagrange$\_$interp which can be called as

where $x_{-}$interp is a vector of interpolation points, $y_{{?}_i\text{n}\text{t}\text{e}\text{r}\text{p}}$ is a vector of function values at the interpolation points, and the output y$\_$eval is the vector of values of the Lagrange interpolating polynomial, evaluated on the input points $x_{-}$eval. Now

$1$

consider interpolating the function $f(x)=\frac{1}{1+25x^2}$ on the interval $-1,1$ using as interpolation points $(1)n$ equispaced points starting at $-1$ and ending at $1$ and $(2)n$ Chebyshev nodes $($i$.$e$.,$ the $n$ zeros of the $n-$th order Chebyshev polynomial$).$ Use your function lagrange$\_$interp to compute and plot the Lagrange interpolating polynomial on a very fine grid. Comment on the comparison between the two interpolation approaches as $n$ becomes large, and print the plots you need to illustrate the difference in behavior. Please answer all parts of the question and make sure to include correct and appropriate MATLAB code. Please dont use python, thank you