Question

Use the limit definition of the derivative to find the instantaneous rate of change of f(x)=√5x+√8 at x=2

Answer 1

Given:

`\begin{gathered} f(x)=\sqrt[]{5x}+\sqrt[]{8} \\ x=2 \end{gathered}`

Derivative of function is:

`\begin{gathered} f(x)=\sqrt[]{5x}+\sqrt[]{8} \\ f^(\prime)(x)=\sqrt[]{5}(\frac{1}{2\sqrt[]{x}})+\sqrt[]{8} \\ f^(\prime)(x)=\frac{\sqrt[]{5}}{2\sqrt[]{x}}+\sqrt[]{8} \end{gathered}`

At x=2 then the derivative is: