Suppose we do piecewise interpolation over equally$-$spaced nodes within $[1,4]$ for f $($x$)=1/$x$.$ We would

like to keep the largest error under $103$

$($a$)$ How many nodes are required for piecewise linear interpolation

$($b$)$ How many nodes are required for piecewise quadratic interpolation

$($c$)$ Use Matlab to confirm your calculation in $($a$)$