   Chapter 10.5, Problem 115E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

If the derivative of f is zero at a point, what do you know about the graph of f near that point?

To determine

The interpretation of the function f if it has been provided that its derivative is zero at a point.

Explanation

Given information:

A function f whose derivative is zero at a point.

When the derivative of the function is zero it means that the rate of change of the function is zero means the function has come to an impasse where it is horizontal or parallel to x-axis.

For example:

Consider the function, g(x)=x2

Put x=0 to determine g(x).

g(0)=(0)2g(0)=0

Put x=1 to determine g(x).

g(1)=(1)2g(1)=1

Put x=2 to determine g(x).

g(2)=(2)2g(2)=4

The steps to draw the graph of the function g(x)=x2 are shown below:

Step 1: Mark the points of the function g(x)=x2 computed above.

Step 2: Join the points marked to form a graph of the desired function.

Draw the graph of the function as follows:

Consider the derivative of the function, g(x)=2x:

Put x=0 to determine g(x)

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