HolcombMath

Monday, June 08, 2009

Intro to Calculus (Class 89)

Lesson Title
Lesson for HW 30 (2): The Derivative Function from a Graphical Perspective

Overview
Today is the last day of regular class! (Even Function!!!!) The main focus is becoming better at sketching the graph of derivative functions when given an original function. Students have the opportunity to continue work in the Library with the computers in order to finish Lesson for HW 30, can work together to finish HW 30, or can play a game in class designed to help them become better derivative function artists.
Textbook Sections
§3.1 (Txt. p. 128) An Introduction to the Derivative: Tangents

Vocabulary
function
independent variable
dependent variable
with respect to
rate of change
limit
derivative
area
definite integral
polar graph
Cartesian
f’(x)

Key Attitudes
Math is about using what you know to create something new.

Key Ideas
For any differentiable function f(x), a slope (derivative) can be found for any value of x.
A function can be created using the derivatives (slopes) of another function.
A derivative function is positive on the intervals where the original function is increasing-- in other words, where the slope of the original function is positive.
A derivative function is negative on the intervals where the original function is decreasing-- in other words, where the slope of the original function is negative.
A derivative function is zero on the intervals where the original function is remaining constant-- in other words, where the slope of the original function is zero.
Key Skills
I can explain what is meant by “derivative function”.
I can determine over what interval a function is differentiable given the graph of the function.
When given four graphs, I can determine if any two represent a function and its derivative function.
I can sketch the graph of the derivative function when given the graph of a function.
I can sketch the graph of a function without using a calculator and then create a graph of the derivative function.
Turn-In (#88)
Nothing to turn in

Handouts
No Handouts Posted

Assignment
Lesson for Homework 30
Homework 30
Workshop 27
Disclaimer- The assignment as stated in class is the official assignment. Every effort is made to keep this posting accurate, but you should refer to what was stated in class as the final word.