Chapter 14: Q. 4 (page 896)

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

Short Answer

Expert verified

If $\lim_{x \to c} \frac{f (x) - f (c)}{x - c}$ 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 $y = f (x)$ denote a function f. If c is a number in the domain of f, the

derivative of f at c, denoted by $f' (c),$ is defined as

$f' (c) = \lim_{x \to c} \frac{f (x) - f (c)}{x - c}$ .

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

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

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Filling the blank

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Short Answer

Step by step solution

Step 1. Given Information

Step 2. Filling the blank

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Most popular questions from this chapter

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