Please show work Consider the data x 0 12 1 2 3 y 0 141 1 1

Please show work !!!

Consider the data x 0 1/2 1 2 3 y 0 1/4.1 -1 -1 (a) Find the piecewise linear interpolating function for the data. (b) Find the piecewise quadratic interpo1atng function. (e) Find the natural cubic spline that interpolates the data. (d) Find the not-a-knot interpolating cubic spline. When using (4.73), let x1 = 0, x2=1,x3=3,andz1= 1/2,z2=2. Graph all four cases for 0

Solution

Post one more problem to get the answers to the remaining two parts. Thanks

a) We need to find the function that is piecewise linear for different regions, the function can be described by the given below equations

f(x) = 0.5x for x belonging to [0,0.5]

1.5x - 0.5 for x belonging to [0.5,1]

-2x + 3 for x belonging to [1,2]

b) We need to find the function that is piecewise quadratic for different regions, the function can be described by the given below equations

f(x) = x^2 for x belonging to [0,1]

x^2 - 5x + 5 for x belonging to [1,3]