Chapter 11, Problem 113CR

To determine

To evaluate: whether the given statement is true.

Answer to Problem 113CR

Yes, the given statement is true.

Explanation of Solution

Given:

The expression

  $f\text{'}\left(z\right)$

gives the slope of the tangent line to the graph of ‘ f’ at the point

  $\left(z,f\left(z\right)\right)$ .

To find the slope of the graph, using limit definition of the derivative,

To find the slope of the graph, using limit definition of the derivative,

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

So,

Yes, the given statement is true.