Chapter 5, Problem 55RE

a.

To determine

To evaluate: The value of $F\left(-2\right)$ and $F\left(2\right)$ if $f\left(t\right)=\{\begin{array}{l}t\text{if }-2\le t<0\\ \frac{t^2}{2}\text{if 0}\le t\le 2\end{array}$.

b.

To determine

To find: An expression for $F^{\prime }\left(x\right)$, for $-2\le x<0$ by using the Fundamental theorem of calculus.

c.

To determine

To find: An expression for $F^{\prime }\left(x\right)$, for $0\le x\le 2$ by using the Fundamental theorem of calculus.

d.

To determine

To evaluate: The value of $F^{\prime }\left(-1\right)$ and $F^{\prime }\left(1\right)$ and interpret.

e.

To determine

To evaluate: The value of $F^{″}\left(-1\right)$ and $F^{″}\left(1\right)$.

f.

To determine

To find: A constant C such that $F\left(x\right)=G\left(x\right)+C$.