Explanation The given function is y = x 2 + 3 1 − x . The point where the cure of the function changes from increasing to decreasing is the local maximum and the point where the curve changes from decreasing to increasing is the local minimum of the function. Sketch the graph of the function y = x 2 + 3 1 − x as shown below in Figure 1

5th Edition

ISBN: 8220102019737

Author: YOCCO

Publisher: PEARSON

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 6, Problem 24RE

To determine

To find: The local maximum and local minima of the function y=x2+31−x.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 23RE

Chapter 6, Problem 25RE

Students have asked these similar questions

23. State Bayes' formula. Jaching R. Machine.

(d) Show that A, and A' are tail events.

11. (a) Define the (mathematical and conceptual) definition of conditional probability P(A|B). (b) Explain the product law in conditional probability. (c) Explain the relation between independence and the conditional probability of two sets.

Chapter 6 Solutions

EBK COLLEGE ALGEBRA IN CONTEXT

Ch. 6.1 - Graph the function h(x) = 3x3 + 5x2 x 10 on the...Ch. 6.1 - Graph the function f(x) = 2x3 3x2 6x on the...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - For Exercises 1116, match the polynomial function...Ch. 6.1 - For Exercises 1720, use the equation of the...Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Sketch a graph of any cubic polynomial function...Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Daily Revenue The daily revenue in dollars from...Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Starbucks Using data from 2005 and projected to...Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Salaries The median salary for male workers, in...Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.2 - Find the cubic function that models the data in...Ch. 6.2 - Find the cubic function that is the best fit for...Ch. 6.2 - Prob. 3E Ch. 6.2 - Find the quartic function that is the best fit for...Ch. 6.2 - Prob. 5E Ch. 6.2 - a. Make a scatter plot of the data in the table...Ch. 6.2 - Prob. 7E Ch. 6.2 - a. Find a cubic function that models the data in...Ch. 6.2 - Prob. 9E Ch. 6.2 - a. Graph each of the functions found in Exercise 9...Ch. 6.2 - Prob. 11E Ch. 6.2 - Prob. 12E Ch. 6.2 - Prob. 13E Ch. 6.2 - Prob. 14E Ch. 6.2 - Prob. 15E Ch. 6.2 - Find the cubic function that is the best fit for...Ch. 6.2 - Use unrounded models for graphing and calculations...Ch. 6.2 - Use unrounded models for graphing and calculations...Ch. 6.2 - Prob. 19E Ch. 6.2 - Prob. 20E Ch. 6.2 - Median Age at First Marriage (Source: U.S. Census...Ch. 6.2 - Prob. 22E Ch. 6.2 - Prob. 23E Ch. 6.2 - Inflation Rate The annual changes in the consumer...Ch. 6.2 - Elderly Men in the Workforce The table below gives...Ch. 6.2 - Prob. 26E Ch. 6.2 - Prob. 27E Ch. 6.2 - Consumer Prices The data in the table give the...Ch. 6.2 - Federal Tax Per Capita The table gives the amount...Ch. 6.2 - Japanese Economy The economy of Japan is the third...Ch. 6.2 - Women in the Workforce The following table gives...Ch. 6.2 - Homicide Rates The table gives the U.S. homicide...Ch. 6.2 - Prob. 33E Ch. 6.2 - Prob. 34E Ch. 6.2 - Prob. 35E Ch. 6.2 - Union Membership The table on the next page gives...Ch. 6.2 - Prob. 37E Ch. 6.2 - Medicaid The numbers of thousands of people...Ch. 6.3 - Prob. 1E Ch. 6.3 - Prob. 2E Ch. 6.3 - Prob. 3E Ch. 6.3 - Prob. 4E Ch. 6.3 - Prob. 5E Ch. 6.3 - Prob. 6E Ch. 6.3 - Prob. 7E Ch. 6.3 - Prob. 8E Ch. 6.3 - Prob. 9E Ch. 6.3 - Prob. 10E Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Prob. 15E Ch. 6.3 - Prob. 16E Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Prob. 19E Ch. 6.3 - Prob. 20E Ch. 6.3 - Prob. 21E Ch. 6.3 - Prob. 22E Ch. 6.3 - Prob. 23E Ch. 6.3 - Prob. 24E Ch. 6.3 - Prob. 25E Ch. 6.3 - Prob. 26E Ch. 6.3 - Prob. 27E Ch. 6.3 - Prob. 28E Ch. 6.3 - Prob. 29E Ch. 6.3 - Prob. 30E Ch. 6.3 - Prob. 31E Ch. 6.3 - Prob. 32E Ch. 6.3 - Prob. 33E Ch. 6.3 - Prob. 34E Ch. 6.3 - Prob. 35E Ch. 6.3 - Prob. 36E Ch. 6.3 - Prob. 37E Ch. 6.3 - Prob. 38E Ch. 6.3 - Constructing a Box A box can be formed by cutting...Ch. 6.3 - Prob. 40E Ch. 6.3 - Prob. 41E Ch. 6.3 - Prob. 42E Ch. 6.3 - Prob. 43E Ch. 6.3 - Prob. 44E Ch. 6.3 - Prob. 45E Ch. 6.3 - Prob. 46E Ch. 6.3 - Prob. 47E Ch. 6.3 - Prob. 48E Ch. 6.3 - Prob. 49E Ch. 6.3 - Prob. 50E Ch. 6.4 - In Exercises 14, use synthetic division to find...Ch. 6.4 - Prob. 2E Ch. 6.4 - Prob. 3E Ch. 6.4 - Prob. 4E Ch. 6.4 - Prob. 5E Ch. 6.4 - Prob. 6E Ch. 6.4 - Prob. 7E Ch. 6.4 - Prob. 8E Ch. 6.4 - Prob. 9E Ch. 6.4 - Prob. 10E Ch. 6.4 - Prob. 11E Ch. 6.4 - Prob. 12E Ch. 6.4 - Prob. 13E Ch. 6.4 - Prob. 14E Ch. 6.4 - In Exercises 1316, find one solution graphically...Ch. 6.4 - Prob. 16E Ch. 6.4 - Prob. 17E Ch. 6.4 - Prob. 18E Ch. 6.4 - Prob. 19E Ch. 6.4 - Prob. 20E Ch. 6.4 - Prob. 21E Ch. 6.4 - Prob. 22E Ch. 6.4 - Prob. 23E Ch. 6.4 - In Exercises 2124, find all rational zeros of the...Ch. 6.4 - Prob. 25E Ch. 6.4 - Prob. 26E Ch. 6.4 - Prob. 27E Ch. 6.4 - Solve each of the equations in Exercises 2530...Ch. 6.4 - Prob. 29E Ch. 6.4 - Prob. 30E Ch. 6.4 - Prob. 31E Ch. 6.4 - In Exercises 3136, use synthetic division and...Ch. 6.4 - Prob. 33E Ch. 6.4 - Prob. 34E Ch. 6.4 - Prob. 35E Ch. 6.4 - Prob. 36E Ch. 6.4 - Drunk Driving Crashes Suppose the total number of...Ch. 6.4 - Prob. 38E Ch. 6.4 - Prob. 39E Ch. 6.4 - Births The number of births to females in the...Ch. 6.4 - Prob. 41E Ch. 6.4 - Personal Savings The model y = 0.000447x3 ...Ch. 6.5 - Give the equations of any (a) vertical and (b)...Ch. 6.5 - Prob. 2E Ch. 6.5 - Prob. 3E Ch. 6.5 - Prob. 4E Ch. 6.5 - Prob. 5E Ch. 6.5 - Prob. 6E Ch. 6.5 - Prob. 7E Ch. 6.5 - Prob. 8E Ch. 6.5 - Prob. 9E Ch. 6.5 - Prob. 10E Ch. 6.5 - Prob. 11E Ch. 6.5 - Prob. 12E Ch. 6.5 - Prob. 13E Ch. 6.5 - Prob. 14E Ch. 6.5 - Prob. 15E Ch. 6.5 - Prob. 16E Ch. 6.5 - Prob. 17E Ch. 6.5 - Prob. 18E Ch. 6.5 - Prob. 19E Ch. 6.5 - Prob. 20E Ch. 6.5 - Prob. 21E Ch. 6.5 - Prob. 22E Ch. 6.5 - Prob. 23E Ch. 6.5 - Prob. 24E Ch. 6.5 - Prob. 25E Ch. 6.5 - Prob. 26E Ch. 6.5 - Prob. 27E Ch. 6.5 - Prob. 28E Ch. 6.5 - Prob. 29E Ch. 6.5 - Prob. 30E Ch. 6.5 - Prob. 31E Ch. 6.5 - Prob. 32E Ch. 6.5 - Prob. 33E Ch. 6.5 - Prob. 34E Ch. 6.5 - Prob. 35E Ch. 6.5 - Prob. 36E Ch. 6.5 - Prob. 37E Ch. 6.5 - Prob. 38E Ch. 6.5 - Prob. 39E Ch. 6.5 - Prob. 40E Ch. 6.5 - Prob. 41E Ch. 6.5 - Average Cost The average cost per unit for the...Ch. 6.5 - Prob. 43E Ch. 6.5 - Prob. 44E Ch. 6.5 - Prob. 45E Ch. 6.5 - Prob. 46E Ch. 6.5 - Prob. 47E Ch. 6.5 - Prob. 48E Ch. 6.5 - Prob. 49E Ch. 6.5 - Prob. 50E Ch. 6.5 - Prob. 51E Ch. 6.5 - Prob. 52E Ch. 6.5 - Prob. 53E Ch. 6.5 - Prob. 54E Ch. 6.5 - Age at First Marriage The table that follows shows...Ch. 6.5 - Fences Suppose that a rectangular field is to have...Ch. 6.5 - Prob. 57E Ch. 6.5 - Prob. 58E Ch. 6.6 - Prob. 1E Ch. 6.6 - Prob. 2E Ch. 6.6 - Prob. 3E Ch. 6.6 - Prob. 4E Ch. 6.6 - In Exercises 116, use algebraic and/or graphical...Ch. 6.6 - Prob. 6E Ch. 6.6 - Prob. 7E Ch. 6.6 - Prob. 8E Ch. 6.6 - Prob. 9E Ch. 6.6 - Prob. 10E Ch. 6.6 - Prob. 11E Ch. 6.6 - Prob. 12E Ch. 6.6 - Prob. 13E Ch. 6.6 - Prob. 14E Ch. 6.6 - Prob. 15E Ch. 6.6 - Prob. 16E Ch. 6.6 - For Exercises 1720, use the graph of y = f(x) to...Ch. 6.6 - Prob. 18E Ch. 6.6 - Prob. 19E Ch. 6.6 - Prob. 20E Ch. 6.6 - Prob. 21E Ch. 6.6 - Prob. 22E Ch. 6.6 - Prob. 23E Ch. 6.6 - Prob. 24E Ch. 6.6 - Prob. 25E Ch. 6.6 - Combine factoring with graphical and/or numerical...Ch. 6.6 - Prob. 27E Ch. 6.6 - 28. Average Cost The average cost per set for the...Ch. 6.6 - Prob. 29E Ch. 6.6 - Prob. 30E Ch. 6.6 - Prob. 31E Ch. 6.6 - Prob. 32E Ch. 6.6 - Prob. 33E Ch. 6.6 - Prob. 34E Ch. 6.6 - Population Suppose the number of employees of a...Ch. 6 - For Exercises 14, (a) give the degree of the...Ch. 6 - For Exercises 14, (a) give the degree of the...Ch. 6 - Prob. 3TE Ch. 6 - Prob. 4TE Ch. 6 - Prob. 5TE Ch. 6 - Prob. 6TE Ch. 6 - Prob. 7TE Ch. 6 - Prob. 8TE Ch. 6 - Prob. 9TE Ch. 6 - Prob. 10TE Ch. 6 - Prob. 11TE Ch. 6 - Prob. 12TE Ch. 6 - Prob. 13TE Ch. 6 - Prob. 14TE Ch. 6 - In Exercises 1116, simplify each rational...Ch. 6 - Prob. 16TE Ch. 6 - Prob. 17TE Ch. 6 - Prob. 18TE Ch. 6 - Prob. 19TE Ch. 6 - Prob. 20TE Ch. 6 - Prob. 21TE Ch. 6 - Prob. 22TE Ch. 6 - Prob. 23TE Ch. 6 - Prob. 24TE Ch. 6 - Prob. 25TE Ch. 6 - Prob. 26TE Ch. 6 - Prob. 27TE Ch. 6 - Prob. 28TE Ch. 6 - Prob. 29TE Ch. 6 - Prob. 30TE Ch. 6 - Prob. 31TE Ch. 6 - Prob. 32TE Ch. 6 - Prob. 33TE Ch. 6 - Prob. 34TE Ch. 6 - Prob. 35TE Ch. 6 - Prob. 36TE Ch. 6 - Prob. 37TE Ch. 6 - Prob. 38TE Ch. 6 - Prob. 39TE Ch. 6 - Prob. 40TE Ch. 6 - In Exercises 3841, perform the long division. 41....Ch. 6 - Prob. 1RE Ch. 6 - Prob. 2RE Ch. 6 - Prob. 3RE Ch. 6 - Prob. 4RE Ch. 6 - Prob. 5RE Ch. 6 - Prob. 6RE Ch. 6 - Prob. 7RE Ch. 6 - Prob. 8RE Ch. 6 - Solve x4 x3 20x2 = 0.Ch. 6 - Prob. 10RE Ch. 6 - Prob. 11RE Ch. 6 - Prob. 12RE Ch. 6 - Prob. 13RE Ch. 6 - Prob. 14RE Ch. 6 - Prob. 15RE Ch. 6 - Prob. 16RE Ch. 6 - Prob. 17RE Ch. 6 - Prob. 18RE Ch. 6 - Find one solution of 3x3 x2 12x + 4 = 0...Ch. 6 - Find one solution of 2x3 + 5x2 4x 3 = 0...Ch. 6 - Prob. 21RE Ch. 6 - Prob. 22RE Ch. 6 - Prob. 23RE Ch. 6 - Prob. 24RE Ch. 6 - Prob. 25RE Ch. 6 - Prob. 26RE Ch. 6 - Prob. 27RE Ch. 6 - Prob. 28RE Ch. 6 - Prob. 29RE Ch. 6 - Prob. 30RE Ch. 6 - Prob. 31RE Ch. 6 - Prob. 32RE Ch. 6 - Prob. 33RE Ch. 6 - Revenue The monthly revenue for a product is given...Ch. 6 - Prob. 35RE Ch. 6 - Prob. 36RE Ch. 6 - Prob. 37RE Ch. 6 - Prob. 38RE Ch. 6 - Foreign Born Population The table on the following...Ch. 6 - Prob. 40RE Ch. 6 - Prob. 41RE Ch. 6 - Break-Even The daily profit in dollars for a...Ch. 6 - Starbucks The table gives the total number of...Ch. 6 - Drugs in the Bloodstream The concentration of a...Ch. 6 - Prob. 45RE Ch. 6 - Prob. 46RE Ch. 6 - Prob. 47RE Ch. 6 - Prob. 48RE Ch. 6 - Prob. 49RE Ch. 6 - Prob. 50RE Ch. 6 - Prob. 51RE Ch. 6 - Prob. 52RE Ch. 6 - Prob. 53RE Ch. 6 - Cost-Benefit The percent p of particulate...

Knowledge Booster

$Algebra$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.

The local maximum and local minima of the function y = x 2 + 3 1 − x .

Solution Summary: The author explains the local maximum and local minima of the function y=x2+31-x

Concept explainers

Videos

To find: The local maximum and local minima of the function y=x2+31−x.

Want to see the full answer?

Chapter 6 Solutions