Given:
[tex]f(t)=8-\frac{3}{5t},(\frac{1}{2},\frac{34}{5})[/tex]
To find:
[tex]f^{\prime}(\frac{1}{2})[/tex]
Explanation:
Finding the first derivative we get,
[tex]\begin{gathered} f^{\prime}(t)=0-\frac{3\cdot(-t^{-2})}{5} \\ f^{\prime}(t)=\frac{3}{5t^2} \end{gathered}[/tex]
Substituting
[tex]\frac{1}{2}[/tex]
We get,
[tex]\begin{gathered} f^{\prime}(\frac{1}{2})=\frac{3}{5(\frac{1}{2})^2} \\ =\frac{3}{5\times\frac{1}{4}} \\ =\frac{12}{5} \end{gathered}[/tex]
Final answer: The value is,
[tex]f^{\prime}(\frac{1}{2})=\frac{12}{5}[/tex]
