2.5_Solving_Problems_Involving_Rates_of_Change

# 2.5_Solving_Problems_Involving_Rates_of_Change - on this...

This preview shows pages 1–2. Sign up to view the full content.

2.5 Solving Problems Involving Rates of Change.notebook 1 September 22, 2009 2.5 Solving Problems Involving Rates of Change Recall: Instantaneous rate of change = slope of tangent Tangent Line: a line which only touches the curve at one point Example #1: Consider the graph of the function shown. (a) Determine whether the instantaneous rate of change is positive or negative at each of the indicated points. (b) Estimate the instantaneous rate of change at: (i) x = -3 (ii) x = 2 (c) What type of points exist at x = -3 and at x = 2? What do you remember about intervals of increase and decrease? The instantaneous rate of change is zero at both the maximum and the minimum point. What type of tangent is drawn at a maximum or minimum point? As a curve increases, the slopes of the tangents to the curve are on this interval.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: on this interval. At a maximum point, the slopes of the tangents must change from to . At a minimum point, the slopes of the tangents must change from to . 2.5 Solving Problems Involving Rates of Change.notebook 2 September 22, 2009 Example #2: For the function f(x) = x 3- 27 x + 1, verify that the point (-3, 55) is either a maximum or a minimum. Example #3: A football is kicked into the air such that its height, h , in metres, after t seconds can be modeled by the function: h(t) = -4.9 t 2 + 26.95 t + 152. (a) Find the time when the football reaches its maximum height. (b) Use the slopes of the tangents to verify that this point is a maximum. Assigned Work: page 112 #3, 4, 5ac, 6ce, 7, 9, 10, 11...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern