Runge's function is written as 𝑓(𝑥)= 1/(1+25𝑥^2) (a) Develop a plot of this function for the int

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Runge's function is written as
𝑓(𝑥)= 1/(1+25𝑥^2)
(a) Develop a plot of this function for the interval from 𝑥 =−1 to
1.
(b) Generate and plot the fourth-order Lagrange interpolating
polynomial using
equi-spaced function values corresponding to 𝑥 =−1, −0.5,0,0.5, and
1.
(c) Use the five points from (b) to estimate f(0.8) with first
through fourth-order
Newton interpolating polynomials.
Note:
For part (a) and (b) use MATLAB. In (b) and (c) generate the
polynomial using the
five points i.e., 𝑥 =−1,−0.5,0,0.5,1 and their corresponding values
of f (x). Use
above Runge’s function for calculating the value of f (x) for each
point.