Todays Agenda Upcoming Homework Section 4.4: Curve Sketching - PowerPoint PPT Presentation

Today’s Agenda • Upcoming Homework • Section 4.4: Curve Sketching • Section 4.5: Optimization Problems Lindsey K. Gamard, ASU SoMSS MAT 265: Calculus for Engineers I Fri., 6 November 2015 1 / 5

Upcoming Homework • WeBWorK HW #19: Sections 4.3 and 4.4, due 11/9/2015 • WeBWorK HW #20: Section 4.5, due 11/13/2015 • Written HW K: Section 4.3 #16,24,26,34,45. Due 11/13/2015. Lindsey K. Gamard, ASU SoMSS MAT 265: Calculus for Engineers I Fri., 6 November 2015 2 / 5

Section 4.4 Last time we used the following list of information to help us sketch graphs: 1 Domain 2 Intercepts 3 Symmetry 4 Asymptotes 5 Intervals of Increase or Decrease 6 Local Maximum and Minimum Values 7 Concavity and Points of Inflection Let’s try one last practice problem. Sketch the graph of f ( x ) = 1 + 1 x + 1 x 2 . Lindsey K. Gamard, ASU SoMSS MAT 265: Calculus for Engineers I Fri., 6 November 2015 3 / 5

Section 4.5 Optimization problems are those that allow us to maximize or minimize a certain quantity. The following steps provide an outline of how to solve an optimization problem: 1 Understand the problem. Critically read the problem statement, and determine the knowns, unknowns, and given conditions. 2 Draw a diagram. 3 Introduce notation. Also label the diagram with the notation you have chosen. 4 Express the quantity that you are trying to maximize or minimize in terms of the other variables in the problem. 5 Find the absolute maximum or minimum value of the quantity in question. Lindsey K. Gamard, ASU SoMSS MAT 265: Calculus for Engineers I Fri., 6 November 2015 4 / 5

Section 4.5 Practice Problems 1 A farmer has 2400 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area? 2 A cylindrical can is to be made to hold 1 liter of oil. Find the dimensions that will minimize the cost of the metal to manufacture the can. 3 Find the area of the largest rectangle that can be inscribed in a semicircle of radius r . 4 Find the point on the parabola y 2 = 2 x that is closest to the point (1 , 4). Lindsey K. Gamard, ASU SoMSS MAT 265: Calculus for Engineers I Fri., 6 November 2015 5 / 5