6.2: Applications of Extreme Values Objective: To use the derivative and extreme values to solve optimization problems.

Slides:

Advertisements

Similar presentations

Maxima and Minima in Plane and Solid Figures

Advertisements

solved problems on optimization

AP Calculus Review: Optimization

To optimize something means to maximize or minimize some aspect of it… Strategy for Solving Max-Min Problems 1. Understand the Problem. Read the problem.

Optimization 4.7. A Classic Problem You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What is the maximum area that.

Applications of Differentiation

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.

4.5 Optimization Problems Steps in solving Optimization Problems 1.Understand the Problem Ask yourself: What is unknown? What are the given quantities?

4.6 Optimization The goal is to maximize or minimize a given quantity subject to a constraint. Must identify the quantity to be optimized – along with.

Section 3.7 – Optimization Problems. Optimization Procedure 1.Draw a figure (if appropriate) and label all quantities relevant to the problem. 2.Focus.

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.

Applications of Extrema Lesson 6.2. A Rancher Problem You have 500 feet of fencing for a corral What is the best configuration (dimensions) for a rectangular.

4.7 Applied Optimization Wed Jan 14

CHAPTER 3 SECTION 3.7 OPTIMIZATION PROBLEMS. Applying Our Concepts We know about max and min … Now how can we use those principles?

Section 4.4: Modeling and Optimization

{ ln x for 0 < x < 2 x2 ln 2 for 2 < x < 4 If f(x) =

Section 4.4 Optimization and Modeling

Filling and Wrapping Test Review Finding the Surface Area and Volume of Rectangular Prisms, Cylinders, and Pyramids.

Calculus and Analytical Geometry

4.4 Modeling and Optimization Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly,

4.7 Optimization Problems In this section, we will learn: How to solve problems involving maximization and minimization of factors. APPLICATIONS OF DIFFERENTIATION.

Optimization. Objective  To solve applications of optimization problems  TS: Making decisions after reflection and review.

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.

Optimization Problems

Da Nang-11/2013 Natural Science Department – Duy Tan University Lecturer: Ho Xuan Binh Optimization Problems. In this section, we will learn: How to solve.

Section 4.5 Optimization and Modeling. Steps in Solving Optimization Problems 1.Understand the problem: The first step is to read the problem carefully.

Optimization Problems Example 1: A rancher has 300 yards of fencing material and wants to use it to enclose a rectangular region. Suppose the above region.

 Snap together cubes to create a solid rectangular figure.  How long is your figure?  How wide is your figure?  What is the height of your figure?

Optimization Problems

MTH 251 – Differential Calculus Chapter 4 – Applications of Derivatives Section 4.6 Applied Optimization Copyright © 2010 by Ron Wallace, all rights reserved.

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

Applied max and min. 12” by 12” sheet of cardboard Find the box with the most volume. V = x(12 - 2x)(12 - 2x)

Optimization Problems Section 4-4. Example  What is the maximum area of a rectangle with a fixed perimeter of 880 cm? In this instance we want to optimize.

2.7 Mathematical Models. Optimization Problems 1)Solve the constraint for one of the variables 2)Substitute for the variable in the objective Function.

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

4.4 Modeling and Optimization, p. 219 AP Calculus AB/BC.

Sec 4.6: Applied Optimization EXAMPLE 1 An open-top box is to be made by cutting small congruent squares from the corners of a 12-in.-by-12-in. sheet of.

Optimization Problems 1.Identify the quantity you’re optimizing 2.Write an equation for that quantity 3.Identify any constraints, and use them to get the.

Sec 4.7: Optimization Problems EXAMPLE 1 An open-top box is to be made by cutting small congruent squares from the corners of a 12-in.-by-12-in. sheet.

Measuring Area.  Area: The number of square units that can be contained on a surface. Imperial area units > Inches in 2 > Feet ft 2 > Yards yd 2.

STEPS IN SOLVING OPTIMIZATION PROBLEMS 1.Understand the Problem The first step is to read the problem carefully until it is clearly understood. Ask yourself:

Optimization Problems. A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along.

Sect. 3-7 Optimization.

Aim: How do we solve optimization problems? A rectangular enclosure is constructed using a barn wall as one side and 63 m of fencing for the other three.

Optimization Buffalo Bill’s Ranch, North Platte, Nebraska

4.5 Optimization II Dr. Julia Arnold

Ch. 5 – Applications of Derivatives

OPTIMIZATION PROBLEMS

2.4 Quadratic Models.

Copyright © 2006 Pearson Education, Inc

Optimizing Area/SA/Volume

4.5 Optimization II Dr. Julia Arnold

4.7 Modeling and Optimization

Honors Calculus 4.8. Optimization.

Calculus I (MAT 145) Dr. Day Wednesday Nov 8, 2017

Calculus I (MAT 145) Dr. Day Friday Nov 10, 2017

Applications of Extrema

Optimization Chapter 4.4.

7. Optimization.

4.6 Optimization The goal is to maximize or minimize a given quantity subject to a constraint. Must identify the quantity to be optimized – along with.

APPLICATIONS OF DIFFERENTIATION

Sec 4.7: Optimization Problems

Calculus I (MAT 145) Dr. Day Wednesday March 27, 2019

Calculus Review: Related Rates & Optimization

Copyright © Cengage Learning. All rights reserved.

4.5 Optimization Problems

Presentation transcript:

6.2: Applications of Extreme Values Objective: To use the derivative and extreme values to solve optimization problems.

In optimization problems, we are looking for the largest or smallest value a function can take. General Procedure for Optimization Problems: 1.Draw a diagram, if possible, and label the various unknown quantities that you will need. Figure out what needs to be maximized or minimized. 2.Write down the information given that is true regardless of the situation. Usually it is a fixed value or some sort of constraint. Write an equation to model this info. 3.Write a formula for what you are looking to maximize or minimize. 4.Rewrite your equation from step 2 in terms of a single variable. Substitute this expression into equation from step 3. 5.Be sure to check to see if there are any restrictions on the domain. These restrictions could indicate a closed interval. 6.Find the extreme values of the function that needs to be maximized or minimized.

Useful Formulas to Review Rectangular Prism: SA= 2lw + 2lh+ 2wh V=lwh Distance Formula: Cylinder: SA = 2πr 2 + 2πrh V= πr 2 h

EXAMPLES: 1. We need to enclose a rectangular field with a fence. We have 500 ft of fencing material and a building is on one side of the field so we won’t need any fencing. Determine the dimensions of the field that will enclose the largest area.

2. We want to construct a box whose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft 2 and the material used to build the sides cost $6/ft 2. If the box must have a volume of 50ft 3, determine the dimensions that will minimize the cost to build the box.

3. A window is being built and the bottom is a rectangle and the top is a semicircle. If there is 12 meters of framing material, what must the dimensions be to let in the most light?