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.

Slides:

Advertisements

Similar presentations

3.7 Modeling and Optimization

Advertisements

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

OPTIMIZATION PROBLEMS Section 3.7. When you are done with your homework, you should be able to… Solve applied minimum and maximum problems.

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.

3.7 Optimization Problems

MAX - Min: Optimization AP Calculus. OPEN INTERVALS: Find the 1 st Derivative and the Critical Numbers First Derivative Test for Max / Min –TEST POINTS.

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.

Reminder: The Extreme Value Theorem states that every continuous function on a closed interval has both a maximum and a minimum value on that interval.

Sec 2.5 – Max/Min Problems – Business and Economics Applications

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.

Using Calculus to Solve Optimization Problems

4.7 FORMING FUNCTIONS FROM VERBAL DESCRIPTIONS

Applied Max and Min Problems Objective: To use the methods of this chapter to solve applied optimization problems.

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

Applied Max and Min Problems

Section 14.2 Application of Extrema

Section 4.4: Modeling and Optimization

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

Do Now: ….. greatest profit ….. least cost ….. largest ….. smallest

4.7 Optimization Problems

Calculus and Analytical Geometry

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

Lesson 4-7 Optimization Problems. Ice Breaker Using a blank piece of paper: Find the extrema (maximum) of A(w) = 2400w – 2w² A’(w) = 2400 – 4w A’(w) =

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 Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999.

Aim: Curve Sketching Do Now: Worksheet Aim: Curve Sketching.

Optimization Section 4.7 Optimization the process of finding an optimal value – either a maximum or a minimum under strict conditions.

Optimization Problems

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

Warm up 9/10/14 a) Find all relative extrema using the 2 nd derivative test: b) Find any points of inflection and discuss the concavity of the graph.

Optimization Problems

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 -

Section 4.7. Optimization – the process of finding an optimal value- either a maximum or a minimum under strict conditions Problem Solving Strategy –

Copyright © Cengage Learning. All rights reserved. Applications of Differentiation.

2.? Calculus Drill 1/11/10 zFind two positive numbers that satisfy the given requirements z(a) the product is 192 and the sum is a minimum z(b) the product.

2/14/2016 Perkins AP Calculus AB Day 12 Section 3.7.

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.

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

Calculus Section 4.5 Solve max/min problems Recall: The max/min value of a function occurs at a point where the derivative of the function is either zero.

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

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

Calculus 3-R-b Review Problems Sections 3-5 to 3-7, 3-9.

3.7 Optimization Problems Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999.

4.4 Optimization Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999 With additional.

Sect. 3-7 Optimization.

Honors Calculus 4.8. Optimization.

Applied Max and Min Problems

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

Optimization Problems

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.

Optimization Problems

3.7 Optimization Problems

AP Calculus BC September 29, 2016.

AP Calculus BC September 30, 2016.

Optimization Problems

Optimization Problems

3.7 Optimization Problems

Optimization Rizzi – Calc BC.

Using Calculus to Solve Optimization Problems

3.7: Optimization Homework: p , 19, 21, 29, 33, 47

Sec 4.7: Optimization Problems

3.7 Optimization Problems

3.7 Optimization Problems

Presentation transcript:

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 and so won’t need any fencing. Determine the dimensions of the field that will enclose the largest area.

1. Identify all given quantities and all quantities to be determined. If possible, make a sketch. 2. Write a primary equation for the quantity that is to be maximized or minimized. 3. Reduce the primary equation to one having a single independent variable. This may involve the use of secondary equations relating the independent variables of the primary equation. 4. Determine the feasible domain of the primary equation. That is, determine the values for which the stated problem makes sense. 5. Determine the desired maximum or minimum value by the calc techniques we learned this chapter.

A manufacturer wants to design an open box having a square base and a surface area of 108 square inches. What dimensions will produce a box with maximum volume? h x x

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.

Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart. They are to be stayed by two wires, attached to a single stake, running from ground level to the top of each post. Where should the stake be placed to use the least amount of wire?

 Read 3.7 Page 223 #4, 9, 17, 20, 21, 23, 26, 29, 42, 39