Write a MATLAB script to answer this question, and include the resulting MATLAB graph.

2. Some modeling considerations have mandated a search for a function u(x)=0e1x+2x2 where the unknown coefficients 1 and 2 are expected to be nonpositive. Given are data pairs to be interpolated, (x0,z0),(x1,z1), and (x2,z2), where zi>0,i=0,1,2. Thus, we require u(xi)=zi The function u(x) is not linear in its coefficients, but v(x)=ln(u(x)) is linear in its. (a) Find a quadratic polynomial v(x) that interpolates appropriately defined three data pairs, and then give a formula for u(x) in terms of the original data. [This is a pen-and-paper item; the following one should consume much less of your time.] (b) Write a script to find u for the data (0,1),(1,.9),(3,.5). Give the coefficients i and plot the resulting interpolant over the interval [0,6]. In what way does the curve behave qualitatively differently from a quadratic