Chapter 12.3, Problem 83E

To determine

To match: The function with the graph of its derivative.

Answer to Problem 83E

The correct match of the derivative of the given function with graph is $\left(\text{b}\right)$ .

Explanation of Solution

Given information:

The given function is,

  $f\left(x\right)=\sqrt{x}$

Concept used:

The derivative of the function is calculated as,

  $f^{\prime }\left(x\right)=\underset{h\to 0}{\lim }\frac{f\left(x+h\right)-f\left(x\right)}{h}$

The given function is,

  $f\left(x\right)=\sqrt{x}$

The derivative of the function is the slope of the function, the graph of the derivative function match with $\left(\text{b}\right)$ .

Therefore, the correct match of the derivative of the given function with graphis $\left(\text{b}\right)$ .