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Chapter 2: Q. 3 (page 164)

Explain why it is not a simple task to calculate the slope of the tangent line to a function fat a point x=c. Shouldn鈥檛 calculating the slope of a line be really easy? What goes wrong here?

Short Answer

Expert verified

The slope of the tangent at x=cis not easy to determine because exact value of slope of the tangent can't be determined correctly.

Step by step solution

01

Step 1. Given information

Given a functionf(x).

02

Step 2. Explanation

The slope of a function at any point x=c, is the approaches of rate of change of f(x)with respect to x=c and its nearby points. Since it is just an approach, therefore exact value of slope of the tangent can't be determined correctly. But for any nearby point atx=c+htox=c, ifh鈫�0 the slope of the tangent is approximate.

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