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 x2 .

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

• ptimization 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 y2 = 2x 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