Wednesday, February 29, 2012MAT 121. Wednesday, February 29, 2012MAT 121 (A)For f(x) = 3x 4 + 4x 3 + 1, determine its absolute extreme values over the.

Slides:

Advertisements

Similar presentations

Optimization Problems

Advertisements

Pre – CalcLesson 2.4 Finding Maximums and Minimums of Polynomial Functions For quadratic functions: f(x) = ax 2 + bx + c To fin d the max. or min. 1 st.

Applications of Cubic Functions

SURFACE AREA & VOLUME.

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.

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

Materials Needed: Graphing calculators Graph paper Scissors Rulers Tape Directions: 1.Cut out the box diagram. 2.Remove the shaded corners. 3.Fold along.

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

Quick Quiz True or False

Business and Economic Models

Section 3.3 Optimization Find the absolute extreme values of each function on the given interval. 1. F(x) = x 3 – 6x 2 + 9x +8 on [-1,2] f is continuous.

Whiteboardmaths.com © 2008 All rights reserved

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.

Section 4.4: Modeling and Optimization

MAT 150 – CLASS #21 Topics: Model and apply data with cubic and quartic functions Solve Polynomial Equations Find factors, zero, x-intercepts, and solutions.

Chapter Twelve Multiple Integrals. Calculus Section 12.1 Double Integrals Over Rectangles Goals Goals Volumes and double integrals Volumes and double.

Chapter 3 Application of Derivatives 3.1 Extreme Values of Functions Absolute maxima or minima are also referred to as global maxima or minima.

Welcome to... A Game of X’s and O’s

Powerpoint Jeopardy Domain and Range MappingsFactoring and Solving Quadratics Graphing Quadratics Quadratic Applications Final Jeopardy.

Applications of Quadratic Equations

Friday, February 24, 2012MAT 121. Friday, February 24, 2012MAT 121 How calculate limits? (a) Try subbing in value! (b) Simplify if possible and return.

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

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

Polynomials Area Applications Treasure Hunt Answer Sheet

Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and.

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

12/17/2015 Math 2 Honors - Santowski 1 Lesson 22 – Solving Polynomial Equations Math 2 Honors - Santowski.

Differential Calculus The derivative, or derived function of f(x) denoted f`(x) is defined as h xx + h P Q x y.

17 A – Cubic Polynomials 1: Graphing Basic Cubic Polynomials.

7.3.1 Products and Factors of Polynomials Products and Factors of Polynomials Objectives: Multiply and factor polynomials Use the Factor Theorem.

3.3B Solving Problems Involving Polynomials

Monday, February 27, 2012MAT 121. Monday, February 27, 2012MAT 121 How calculate limits? (a) Try subbing in value! (b) Simplify if possible and return.

CHAPTER Continuity Optimization Problems. Steps in Solving Optimizing Problems : 1.Understand the problem. 2.Draw a diagram. 3.Introduce notation.

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.

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.

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.

Notes Over 1.2 Express the power in words. Then write the meaning. Word Meaning.

2.6 Extreme Values of Functions

Find all critical numbers for the function: f(x) = (9 - x 2 ) 3/5. -3, 0, 3.

AP Calculus Unit 4 Day 7 Optimization. Rolle’s Theorem (A special case of MVT) If f is continuous on [a,b] and differentiable on (a,b) AND f(b)=f(a) Then.

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.

EQ: How are extreme values useful in problem solving situations?

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

Ch. 5 – Applications of Derivatives

1.4 – Extrema and Rates of Change

MAXIMIZING AREA AND VOLUME

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

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

7. Optimization.

Trial and Improvement 100 cm2 Example

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.

Chapter 3: Polynomial Functions

Optimization Problems

At what point is the following function a local minimum? {image}

Open Box Problem Problem: What is the maximum volume of an open box that can be created by cutting out the corners of a 20 cm x 20 cm piece of cardboard?

Application of Differentiation

Sec 4.7: Optimization Problems

2.7 Mathematical Models: Constructing Functions

6.7 Using the Fundamental Theorem of Algebra

Differentiation and Optimisation

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

Presentation transcript:

Wednesday, February 29, 2012MAT 121

Wednesday, February 29, 2012MAT 121 (A)For f(x) = 3x 4 + 4x 3 + 1, determine its absolute extreme values over the interval [−2,1]. (B)If g(x) = x – 2√x: (i) determine its absolute extreme values over the interval [0,9]. (ii) determine its absolute extreme values for all x. (C)For 2006, operating rate of factories, mines, and utilities in a certain region of the country, expressed as a % of full capacity, is given by the function shown below, where 0 ≤ t ≤ 250 is measured in days. On which of the first 250 days of 2006 was the rate the highest?

Wednesday, February 29, 2012MAT 121

Wednesday, February 29, 2012MAT 121

Wednesday, February 29, 2012MAT 121 If exactly 200 people sign up for a charter flight, Leisure World Travel Agency charges $400/person. However, if more than 200 people sign up for the flight (assume this is the case), then each fare is reduced by $1 for each additional person. Hint: Let x denote the number of passengers above 200. Determine the revenue function R(x). Determine how many passengers will result in a maximum revenue for the travel agency. What is the maximum revenue? What would be the fare per passenger in this case?

Wednesday, February 29, 2012MAT 121 An open-topped box is to be created from a rectangular piece of tin that measures 20 cm by 32 cm. The box is created by removing congruent squares from each corner of the rectangle and then folding up the flaps. What is the measure of the largest square that could be removed from each corner? If each cut-out square measures x cm on each side, what is a formula for the volume of the resulting box? What value of x generates the largest volume? What would be the volume in this case?

Wednesday, February 29, 2012MAT 121