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Chapter 14: Q. 4 (page 896)

If limx鈫�cf(x)-f(c)x-cexists, it is called the _____ of f at c.

Short Answer

Expert verified

If limx鈫�cf(x)-f(c)x-c exists, it is called the derivative offatc.

Step by step solution

01

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.

02

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 byf'(c),is defined as

f'(c)=limx鈫�cf(x)-f(c)x-c.

Thus, iflimx鈫�cf(x)-f(c)x-cexists, it is called the derivative offatc.

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Most popular questions from this chapter

Graph each function. Use the graph to find the indicated limit, if it exists.

limx鈫�0f(x),f(x)=ex

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