AP Calculus BC September 30, 2016.

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.
Solving Equations = 4x – 5(6x – 10) -132 = 4x – 30x = -26x = -26x 7 = x.
Objectives: Set up a Linear Programming Problem Solve a Linear Programming Problem.
CHAPTER 3 SECTION 3.7 OPTIMIZATION PROBLEMS. Applying Our Concepts We know about max and min … Now how can we use those principles?
Do Now: ….. greatest profit ….. least cost ….. largest ….. smallest
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) =
3.5 – Solving Systems of Equations in Three Variables.
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 Section 4.7 Optimization the process of finding an optimal value – either a maximum or a minimum under strict conditions.
Warm-Up 3.4 1) Solve the system. 2) Graph the solution.
Copyright © Cengage Learning. All rights reserved. 3 Applications of the Derivative.
Optimization Problems
Constraints Feasible region Bounded/ unbound Vertices
Unit 1 Linear programming. Define: LINEAR PROGRAMMING – is a method for finding a minimum or maximum value of some quantity, given a set of constraints.
MTH 251 – Differential Calculus Chapter 4 – Applications of Derivatives Section 4.6 Applied Optimization Copyright © 2010 by Ron Wallace, all rights reserved.
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.
LINEAR PROGRAMMING 3.4 Learning goals represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret.
A25 & 26-Optimization (max & min problems). Guidelines for Solving Applied Minimum and Maximum Problems 1.Identify all given quantities and quantities.
3-5: Linear Programming. Learning Target I can solve linear programing problem.
3.3 Linear Programming. Vocabulary Constraints: linear inequalities; boundary lines Objective Function: Equation in standard form used to determine the.
Applied max and min. Steps for solving an optimization problem Read the problem drawing a picture as you read Label all constants and variables as you.
Chapter 3 Section 4 Linear Programming Algebra 2 January 29, 2009.
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:
Section 3.5 Linear Programing In Two Variables. Optimization Example Soup Cans (Packaging) Maximize: Volume Minimize: Material Sales Profit Cost When.
3.7 Optimization Problems Buffalo Bill’s Ranch, North Platte, Nebraska Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1999.
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.
Jon Rogawski Calculus, ET First Edition
AP Calculus BC September 12, 2016.
Calculus-Based Optimization Prepared by Lee Revere and John Large
Implicit Differentiation
2-5 Absolute Value Functions and Graphs
4.3 Derivatives and the shapes of graphs 4.5 Curve Sketching
Calculus I (MAT 145) Dr. Day Wednesday Nov 8, 2017
Calculus I (MAT 145) Dr. Day Friday Nov 10, 2017
Optimization Chapter 4.4.
AP Calculus BC September 22, 2016.
AP Calculus BC September 23, 2016.
Differential Equations
AP Calculus BC October 10, 2016.
Applications of Differential Calculus
Differential Equations Separation of Variables
Optimization Problems
Entry Task Consider the function f(x):
Lesson 4-4: Modeling and Optimization
3.7 Optimization Problems
3-3 Optimization with Linear Programming
AP Calculus BC September 29, 2016.
Increasing & Decreasing Functions First Derivative Test
Optimization Problems
Day 6 – Tangent Lines and Derivatives
Optimization and Differentials (Sections 3.7 and 3.9)
AP Calculus BC September 28, 2016.
Optimization Rizzi – Calc BC.
AP Calculus March 10 and 13, 2017 Mrs. Agnew
Warm Up Solve for x:
Unit 7, Lesson 1 Trigonometry / Pre-Calculus
Unit 5: Introduction to Differential Calculus
AP Calculus March 6-7, 2017 Mrs. Agnew
LINEARPROGRAMMING 4/26/2019 9:23 AM 4/26/2019 9:23 AM 1.
3.7: Optimization Homework: p , 19, 21, 29, 33, 47
Sec 4.7: Optimization Problems
Nature does nothing uselessly.
Section 6.3 Day 1 Separation of Variable
3.7 Optimization Problems
4.5 Optimization Problems
3.7 Optimization Problems
Presentation transcript:

AP Calculus BC September 30, 2016

Learning Targets I understand how to apply derivatives to solve a variety of problems. I solved applied optimization problems (determining the maximum or minimum).

Optimization Problems Identify given quantities, quantities to be determined, and make a sketch. Write a primary equation for the quantity to be maximized or minimized. Reduce the primary equation into an equation with a single independent variable. A secondary equation relating the variables of the primary equation may be needed. Determine the feasible domain of the primary equation. Use calculus to determine the optimum value.

Optimization Problems Page 226: 45 Page 226: 49 Page 227: 54 Page 227: 60

No Homework