Chapter 3.2, Problem 5E

Assume that a function $f\left(x\right)$ has been approximated by the degree 5 interpolating polynomial $P\left(x\right)$, using the data points $\left(x_i,f\left(x_i\right)\right)$, where $x_1=0.1$, $x_2=0.2$, $x_3=0.3$, $x_4=0.4$, $x_5=0.5$, $x_6=0.6$ . Do you expect the interpolation error $\left|f\left(x\right)-P\left(x\right)\right|$ to be smaller for $x=0.35$ or for $x=0.55$

? Quantify your answer.