Percent Increase and Decrease Quiz
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Calculus - How Can One Graph Help Describe Another Graph?
This activity incorporates the graphing calculator to help students understand how the behavior of one graph can describe the behavior of another function. Three related equations are entered in y1, y2, and y3 in the graphing calculator. • The original function is entered in y1. • An expression that represents the derivative of y1 is entered in y2. • An expression that represents the derivative of y2 is entered in y3. After graphing y1, y2, and y3 in the same window, a series of questi
10th - 12th, Higher Education
Calculus, Math
Calculus-Making Observations about the Function and Its Derivatives from Graphs
This discovery activity is made up of 5 part plus a closing question. Part I: Students graph a function and its derivative. From the two graphs students observe that when the graph of the derivative of y1 is positive the graph of y1 is increasing and that when the graph of the derivative of y1 is negative the graph of decreasing. Part II: In part I students studied a function with a minimum. In this part students will repeat the same observations but with a function that has a maximum. Part II
10th - 12th, Higher Education
Calculus, Math
Pre-Calculus - Maximizing the Volume of a Cone
This hands-on activity engages the students in constructing a cone from a circle,collecting data on the height and radius of the cone, creating a scatterplot, fitting a curve to the data and then estimating the maximum volume of the cone. Many students are surprised that the scatterplot indicates that the volume first slowly increases and then after a maximum volume occurs the volume quickly decreases. By working with a physical model helps students observe how the height, radius, and volume
11th - 12th, Higher Education
Calculus, Math
Related Rates - Tootsie Pop Lab
Students will measure the change in radius of a tootsie pop, then created a line of best fit to find dr/dt. Finally, students will find dv/dt and talk about when volume is changing the fastest.
10th - 12th
Calculus, Math, Other (Math)
Calculus - Understanding The Derivative Graphically Using Difference Quotients
Students can used their graphing calculators to build an understanding for the formal definition of a derivative (limit as h approaches zero of (f(x+h)-f(x))/h). Students will set up the forward difference quotient, the backward difference quotient, and the symmetric difference quotient approaching the same limit. Then students will let h equal 1, 0.1, 0.01, and 0.001) to notice that all the difference quotients approach one function. The function they are all approaching will be called
10th - 12th, Higher Education
Calculus, Math, PreCalculus
Also included in: Calculus - Understanding the Derivative Bundle
Calculus - Continuity
This activity engages the students in understanding the three parts of the definition for a continuous function at a point by asking a series of questions about several functions. You also might be interested in the Activity Sheet on Continuity and the Intermediate Value Theorem that is available in my store. A recent buyer said "Thank you for providing this resource. I appreciate your time and investment in creating a helpful resource."
11th - 12th, Higher Education
Calculus, Math, PreCalculus
Also included in: Calculus - Continuity Bundle
Volumes of Solids with Known Cross Sections - An Exploration in Calculus
One of the topics that is difficult for students to grasp is finding the volume of a solid with a known cross section. One reason is that students have difficulty with this topic is that they have difficulty drawing the solid. In this activity the students get to build eight different "solids.” This activity focuses on finding the volume of solids that are built on a two-dimensional surface when cross section cut perpendicular to a known shape. The activity uses the region bounded by the x-axis,
10th - 12th, Higher Education
Calculus, Math
Also included in: Calculus - Volume using Known Cross Sections Bundle
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