Question

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

Short answer

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

Step-by-step solution

Step 1. Given Information 

The slope of the tangent line to the graph of a function at a given point is known as the derivative of the function at that given point.

Step 2. Filling the blank 

Let $y=f\left(x\right)$ denote a function f. If c is a number in the domain of f, the

derivative of f at c, denoted by$f\text{'}\left(c\right),$is defined as

$f\text{'}\left(c\right)=\underset{x\to c}{\lim }\frac{f\left(x\right)-f\left(c\right)}{x-c}$.

Thus, if$\underset{x\to c}{\lim }\frac{f\left(x\right)-f\left(c\right)}{x-c}$exists, it is called the derivative offatc.