Answer
See explanation.
Work Step by Step
(a) $F(4)=\int_{4}^{4} \sqrt{9+t^{2}} d t=0$
(b)
\[
F^{\prime}(x)=\sqrt{9+x^{2}}
\]
And therefore:
\[
F^{\prime}(4)=\sqrt{9+4^{2}}=\sqrt{25}=5
\]
(c)
\[
F^{\prime \prime}(x)=\frac{x}{\sqrt{9+x^{2}}}
\]
And therefore:
\[
F^{\prime \prime}(4)=\frac{4}{\sqrt{9+4^{2}}}=\frac{4}{5}
\]
