Question

Find the value of the derivative of the function at the given point.3f(t) = 85t ，（345

Answer 1

Given:

`f(t)=8-(3)/(5t),((1)/(2),(34)/(5))`

To find:

`f^(\prime)((1)/(2))`

Step-by-step explanation:

Finding the first derivative we get,

`\begin{gathered} f^(\prime)(t)=0-(3\cdot(-t^(-2)))/(5) \\ f^(\prime)(t)=(3)/(5t^2) \end{gathered}`

Substituting

`(1)/(2)`

We get,

`\begin{gathered} f^(\prime)((1)/(2))=(3)/(5((1)/(2))^2) \\ =(3)/(5*(1)/(4)) \\ =(12)/(5) \end{gathered}`

Final answer: The value is,

`f^(\prime)((1)/(2))=(12)/(5)`