Chapter 14.4, Problem 4AYU

$\underset{x\to c}{\lim }\frac{f\left(x\right)-f\left(c\right)}{x-c}$ exists, it is called the _________of $f$ at $c$.

To determine

To fill: If $\underset{x\to c}{\text{lim}}\frac{f\left(x\right)-f\left(c\right)}{x-c}$ exists, it is called the _____ of $f$ at $c$.

Answer to Problem 4AYU

Solution:

Derivative.

Explanation of Solution

Given:

We know the derivative of $f$ at the point $x=c$ is: $f^{\prime }\left(c\right)=\underset{x\to c}{\text{lim}}\frac{f\left(x\right)-f\left(c\right)}{x-c}$.