/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 30 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 30

Use a graphing utility to graph the function. Choose a window that allows all relative extrema and points of inflection to be identified on the graph. \(y=x^{-1 / 3}\)

Short Answer

Expert verified
After graphing this function, you'll find out that it doesn't have any local minima or maxima. It has an inflection point at x = 0. For x>0, it curves upwards and for x<0, it curves downwards.

Step by step solution

01

Understanding the Function

Begin by understanding the function \(y=x^{-1/3}\), it is a root cubic function. This means that the function will have a graph that curves upwards for positive values of x and curves downwards for negative values of x.
02

Identify Extrema and Inflection Points

The function \(y=x^{-1/3}\) does not have any relative extrema because it curves upward and downward universally and does not attain a highest value in some interval (maximum) or lowest value in some interval (minimum). Therefore, it has no local maxima or minima. Also, function \(y=x^{-1/3}\) have a point of inflection at x = 0. As for x>0, the function curves upwards and for x<0, it curves downwards.
03

Choose Window for Graph

Choose a window which allows you to clearly see the properties of this function. A window from -10 to 10 on both axes would be suitable.
04

Graphing

Using a graphing utility, graph the function within the window specified. This will give a complete picture of how function behaves for both positive and negative values of x.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Sketch the graph of the function. Choose a scale that allows all relative extrema and points of inflection to be identified on the graph. \(y=x^{4}-2 x^{2}\)

The radius of a sphere is measured to be 6 inches, with a possible error of \(0.02\) inch. Use differentials to approximate the possible error and the relative error in computing the volume of the sphere.

Sketch the graph of the function. Label the intercepts, relative extrema, points of inflection, and asymptotes. Then state the domain of the function. \(y=\frac{x^{3}}{x^{3}-1}\)

Use a graphing utility to graph the function. Choose a window that allows all relative extrema and points of inflection to be identified on the graph. \(y=1-x^{2 / 3}\)

Marginal Analysis, use differentials to approximate the change in cost, revenue, or profit corresponding to an increase in sales of one unit. For instance, in Exercise 29, approximate the change in cost as \(x\) increases from 12 units to 13 units. Then use a graphing utility to graph the function, and use the trace feature to verify your result. \(R=50 x-1.5 x^{2} \quad x=15\)
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.