Upload your code to a file named HW$4\_$Question$4.$py and use this code to solve the following:

a$)$ Plot the Lagrange polynomial interpolation for $f(x)=\sqrt[\phantom{2}]{x},$ using the following

points. Plot both the polynomial and the actual graph of $f(x)$ for $1000$ values of

$x$ between $0$ and $6.$ Upload your plot and name it $"$HW$4\_$Question$4$a$\_$plot.png$"$

$\sqrt[\phantom{2}]{0}=0$

$\sqrt[\phantom{2}]{1}=1$

$\sqrt[\phantom{2}]{2}$~~$1\mathrm{.}4142135624$

$\sqrt[\phantom{2}]{4}=2$

$\sqrt[\phantom{2}]{6}$~~$2\mathrm{.}449489742783$

b$)$ Plot the error in the polynomial approximation from part $($a$)$ and upload it to a

file named $"$HW$4\_$Question$4$b$\_$plot.png$"$