Answer
$$f''(2)= \frac{-4 }{27}$$
Work Step by Step
Given $$f(t)= \sqrt{4t+1}$$
Since
\begin{align*}
f'(t)&=\frac{4}{2\sqrt{4t+1}}=2(4t+1)^{-1/2}\\
f''(t)&=-4(4t+1)^{-3/2}
\end{align*}
then
$$f''(2)=-4(4(2)+1)^{-3/2}=\frac{-4 }{27}$$
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