Example 2 Finding the Maximum Volume Chapter 6.3 A box is to be formed by cutting squares x inches per side from each corner of a square piece of cardboard.

Slides:

Advertisements

Similar presentations

Guidelines for Solving Applied Minimum and Maximum Problems 1.Identify all given quantities and quantities to be determined. If possible, make a sketch.

Advertisements

Example 3 Inverse of a 3 x 3 Matrix Chapter 7.4 Find the inverse of.  2009 PBLPathways.

Lesson 2-4 Finding Maximums and Minimums of Polynomial Functions.

3.7 Optimization Problems

Pg. 98/110 Homework Pg. 127#25 – 28 all Pg. 138#42, 43, 48, 88 – 93 all #58 15 liters of 20% acid and 10 liters of 35% acid # liters of distilled.

Applications of Cubic Functions

17 A – Cubic Polynomials 4: Modeling with Cubics.

Choose the Best Regression Equation

A rectangular dog pen is constructed using a barn wall as one side and 60m of fencing for the other three sides. Find the dimensions of the pen that.

Polynomial Functions Section 2.3. Objectives Find the x-intercepts and y-intercept of a polynomial function. Describe the end behaviors of a polynomial.

4.4 Optimization Finding Optimum Values. A Classic Problem You have 40 feet of fence to enclose a rectangular garden. What is the maximum area that you.

1 Applications of Extrema OBJECTIVE  Solve maximum and minimum problems using calculus. 6.2.

2.8 Analyzing Graphs of Polynomial Functions p. 373

1.7. Who was the roundest knight at King Arthur's Round Table? Sir Cumference.

Pg. 116 Homework Pg. 117#44 – 51 Pg. 139#78 – 86 #20 (-2, 1)#21[0, 3] #22 (-∞, 2]U[3, ∞)#24(-∞, -3]U[½, ∞) #25 (0, 1)#26(-∞, -3]U(1, ∞) #27 [-2, 0]U[4,

Modeling and Optimization

Optimization Practice Problems.

AIM: APPLICATIONS OF FUNCTIONS? HW P. 27 #74, 76, 77, Functions Worksheet #1-3 1 Expressing a quantity as a function of another quantity. Do Now: Express.

Volume word problems Part 2.

Sec 4.5 – Indeterminate Forms and L’Hopital’s Rule Indeterminate Forms L’Hopital’s Rule.

Copyright © 2014, 2010, 2006 Pearson Education, Inc. 1 Chapter 3 Quadratic Functions and Equations.

PRE-ALGEBRA. Reasoning Strategy: Make a Model (10-8) How can you use a model to help solve a problem? Example: A box company makes boxes to hold popcorn.

Example Suppose a firework is launched with an upward velocity of about 80 ft/sec from a height of 224 feet. Its height in feet, h(t), after t seconds.

Volume Performance Task Rectangular Prisms

6.8 Analyzing Graphs of Polynomial Functions

Ch 4.4 Modeling and Optimization Graphical, Numerical, Algebraic by Finney Demana, Waits, Kennedy.

Review: 6.5h Mini-Quiz 1.Solve: An object is dropped from a cliff 480 ft above the ground. Find the time t (in sec) for the object to reach the ground.

Sullivan PreCalculus Section 2.6 Mathematical Models: Constructing Functions Objectives Construct and analyze functions.

Miss Battaglia AB/BC Calculus. We need to enclose a field with a fence. We have 500 feet of fencing material and a building is on one side of the field.

C2: Maxima and Minima Problems

Applications and Modeling with Quadratic Equations

Example 4 Continuous Versus Annual Compounding of Interest Chapter 5.5 a.For each of 9 years, compare the future value of an investment of $1000 at 8%

EOQ REVIEW #2 Hoops Exponents RadicalsPolynomials Factoring Word Problems Q 1 pt. Q 2 pt. Q 3 pt. Q 4 pt. Q 5 pt. Q 1 pt. Q 2 pt. Q 3 pt. Q 4 pt. Q 5.

Text – p594 #1-21 odds. Chapter 9: Polynomial Functions Chapter Review Mrs. Parziale.

Notes Over 6.8 Using x-Intercepts to Graph a Polynomial Function Graph the function. x-inter: 1, -2 End behavior: degree 3 L C: positive Bounces off of.

Graphing Polynomials. Total number of roots = __________________________________. Maximum number of real roots = ________________________________. Maximum.

What is the Largest – Volume, Open –Top, Rectangular Box You can make from…. a sheet of paper, a piece of poster board a sheet of cardboard….

Polynomial Functions and Models

Matt 6-7 pm Week 6, Session 2 MATH 1300 SI. Sundays: 7:05-8:05 Mondays: 6:00-7:00 Wednesdays: 6:00-7:00 Morton MATH 1300 SI.

Jeopardy Math II Ms. Brown’s 2 nd Period Class. Quadratics Factoring Square Roots Quadratic Formula Graphically Word Problems FINAL.

3.3B Solving Problems Involving Polynomials

Optimization. First Derivative Test Method for finding maximum and minimum points on a function has many practical applications called Optimization -

Applications of Cubic Functions Volume of a Open Box. Suppose you are trying to make an open-top box out of a piece of cardboard that is 12 inches by.

Example 2 Average Cost Chapter 6.6 The average cost per set for the production of 42-inch plasma televisions is given by where x is the number of hundreds.

Make a Model A box company makes boxes to hold popcorn. Each box is made by cutting the square corners out of a rectangular sheet of cardboard. The rectangle.

A25 & 26-Optimization (max & min problems). Guidelines for Solving Applied Minimum and Maximum Problems 1.Identify all given quantities and quantities.

Building Boxes What is the largest volume open top box that you can build from an 8 ½ by 11 inch sheet of paper?

Optimization Problems

Maximum Volume of a Box An Investigation Maximum volume of a box From a square piece of cardboard of side 20 cm small corners of side x are cut off.

Optimization. A company manufactures and sells x videophones per week. The weekly price-demand and cost equations are What price should the company charge.

Analyzing Graphs of Polynomial Functions

Choose the Best Regression Equation

MAXIMIZING AREA AND VOLUME

Optimization Chapter 4.4.

6.8 Analyzing Graphs of Polynomial Functions

Trial and Improvement 100 cm2 Example

Factoring to Solve Quadratic Equations

3.6 Mathematical Models: Constructing Functions

2.7 Mathematical Models: Constructing Functions

From a square sheet of paper 20 cm by 20 cm, we can make a box without a lid. We do this by cutting a square from each corner and folding up the flaps.

ONE THIRD of the area of the base, B, times the height, h

Chapters 1 & 2 Review Day.

Polynomials: Application

Day 168 – Cubical and cuboidal structures

5.4 Modeling and Optimization

2.7 Mathematical Models: Constructing Functions

6.7 Using the Fundamental Theorem of Algebra

P.3B Polynomials and Special Factoring

Presentation transcript:

example 2 Finding the Maximum Volume Chapter 6.3 A box is to be formed by cutting squares x inches per side from each corner of a square piece of cardboard that is 24 inches on each side and folding up the sides. This will give a box whose height is x inches, with the length of each side of the bottom 2x less than the original length of the cardboard. Using V = lwh, its volume is given by where x is length of the side of the square that is cut out.  2009 PBLPathways

A box is to be formed by cutting squares x inches per side from each corner of a square piece of cardboard that is 24 inches on each side and folding up the sides. This will give a box whose height is x inches, with the length of each side of the bottom 2x less than the original length of the cardboard. Using V = lwh, its volume is given by where x is length of the side of the square that is cut out.

 2009 PBLPathways a.Use the factors of V to find the values of x that give volume 0. b.Graph the function that gives the volume as a function of the side of the square that is cut out over an x-interval that includes the x-values found in part (a). c.What input values make sense for this problem (that is, actually result in a box)? d.Graph the function using the input values that make sense for the problem (found in part (c)). e.Use technology to determine the size of the squares that should be cut out to give the maximum volume.

 2009 PBLPathways a.Use the factors of V to find the values of x that give volume 0.

 2009 PBLPathways a.Use the factors of V to find the values of x that give volume 0.

 2009 PBLPathways a.Use the factors of V to find the values of x that give volume 0.

 2009 PBLPathways a.Use the factors of V to find the values of x that give volume 0.

 2009 PBLPathways a.Use the factors of V to find the values of x that give volume 0.

 2009 PBLPathways b.Graph the function that gives the volume as a function of the side of the square that is cut out over an x-interval that includes the x-values found in part (a). x V

 2009 PBLPathways b.Graph the function that gives the volume as a function of the side of the square that is cut out over an x-interval that includes the x-values found in part (a). x V

 2009 PBLPathways b.Graph the function that gives the volume as a function of the side of the square that is cut out over an x-interval that includes the x-values found in part (a). x V

 2009 PBLPathways c.What input values make sense for this problem (that is, actually result in a box)? All dimensions must be positive.

 2009 PBLPathways c.What input values make sense for this problem (that is, actually result in a box)? All dimensions must be positive.

 2009 PBLPathways c.What input values make sense for this problem (that is, actually result in a box)? All dimensions must be positive.

 2009 PBLPathways c.What input values make sense for this problem (that is, actually result in a box)? All dimensions must be positive.

 2009 PBLPathways c.What input values make sense for this problem (that is, actually result in a box)? All dimensions must be positive.

 2009 PBLPathways c.What input values make sense for this problem (that is, actually result in a box)? All dimensions must be positive.

 2009 PBLPathways d.Graph the function using the input values that make sense for the problem (found in part (c)). x V

 2009 PBLPathways d.Graph the function using the input values that make sense for the problem (found in part (c)). x V

 2009 PBLPathways e.Use technology to determine the size of the squares that should be cut out to give the maximum volume. x V

 2009 PBLPathways e.Use technology to determine the size of the squares that should be cut out to give the maximum volume. x V (4, 1024)

 2009 PBLPathways e.Use technology to determine the size of the squares that should be cut out to give the maximum volume. x V (4, 1024) 4 16