Please explain how to solve.

$(5$ points$)$ Let $f(x)$ be a function that satisfies $|f^{\text{'}\text{'}}(x)|6$ on the interval $3,7.$ Choose the smallest $n$ so that we can be sure that $E_M=|M_n-{\displaystyle \underset{3}{\overset{7}{}}}f(x)dx|0\mathrm{.}002,$ where $M_n$ is the midpoint approximation with $n$ intervals.

A$.n=106$

B$.n=90$

C$.n=84$

D$.n=26$

E$.n=140$

$(5$ points$)$ Find the Trapezoidal rule estimate of ${\displaystyle \underset{2}{\overset{5}{}}}f(x)dx$ with $n=6.$

A$.\frac{3}{2}(f(2)4f(2\mathrm{.}5)2f(3)4f(3\mathrm{.}5)2f(4)4f(4\mathrm{.}5)f(5))$

B$.\frac{1}{2}(f(2\mathrm{.}25)f(2\mathrm{.}75)f(3\mathrm{.}75)f(4\mathrm{.}25)f(4\mathrm{.}75))$

C$.\frac{1}{6}(f(2)2f(2\mathrm{.}5)2f(3)2f(3\mathrm{.}5)2f(4)2f(4\mathrm{.}5)f(5))$

D$.\frac{1}{4}(f(2)2f(2\mathrm{.}5)2f(3)2f(3\mathrm{.}5)2f(4)2f(4\mathrm{.}5)f(5))$

E$.\frac{1}{2}(f(2)f(2\mathrm{.}5)f(3)f(3\mathrm{.}5)f(4)f(4\mathrm{.}5))$