Chapter 5.5, Problem 1ES

Find the value of

(a) ${\displaystyle \underset{k=1}{\overset{n}{\sum }}f\left(x_k^{*}\right)\Delta x}$

(b) $\max \Delta x_k$ .

$f\left(x\right)=x+1;a=0,b=4;n=3;\Delta x_1=1,\Delta x_2=1,\Delta x_3=2;x_1^{*}=\frac{1}{3},x_2^{*}=\frac{3}{2},x_3^{*}=3$