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 $f$ at a point $x = c$ . Shouldn’t calculating the slope of a line be really easy? What goes wrong here?

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information

Given a function $f (x)$ .

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 at $x = c + h$ to $x = c$ , if $h \to 0$ the slope of the tangent is approximate.

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

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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’t calculating the slope of a line be really easy? What goes wrong here?

Short Answer

Step by step solution

Step 1. Given information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

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