Q$3.$ The power generated by a windmill varies with the wind speed. In an experiment, the five measurements were obtained:

$\backslash$table$[[$Wind Speed $(k\frac{m}{h}),22,35,48,61,74],[$Electric Power $(W),320,490,540,500,480]]$

a$)$ Determine the fourth$-$order polynomial in the Lagrange from that passes through the points. Use the polynomial to calculate the power at wind speed of $42k\frac{m}{h}.$

b$)$ Determine the fourth$-$order Newton's interpolating polynomial that passes through the data points. Use the polynomial to calculate the power at a wind speed of $26k\frac{m}{h}.$