Station $3$:

For each problem, find the average value of the function over the given interval. Then, find the values of $c$ that satisfy the Mean Value Theorem for Integrals.

$11$

For each problem, find $F^{\text{'}}(x).$

$F(x)={\displaystyle \underset{0}{\overset{x}{}}}(-t^{2}2t-1)dt$

$F(x)={\displaystyle \underset{1}{\overset{x^3}{}}}(t-1{)}^{\frac{1}{2}}dt{F}^{\text{'}}(x)=$

$F(x)={\displaystyle \underset{x}{\overset{x^2}{}}}secttantdt$