Answer
$a)$ = $1.500$
$b)$ = $0.000$
Work Step by Step
$a)$
$f'(x)$ = $6x^{2}$
$f''(x)$ = $12x$
$\frac{(b-a)^{3}}{12n^{2}}$$f''(x)$ = $\frac{2^{3}}{12(4)^{2}}$$(36)$
= $1.500$
$b)$
$f^{3}(x)$ = $12$
$f^{4}(x)$ = $0$
$\frac{(b-a)^{5}}{180n^{4}}$$f^{4}(x)$ = $\frac{2^{5}}{180(4)^{4}}$$(0)$
= $0.000$
