Work from Thursday March 5th, 2009 in vLearning Calculus

1. MCV4U ­ Curve Sketching Day 1
Consider the function f (x) = 2x3 ­ 9x2 ­ 108x + 2 and discuss the following
questions ...
(1) Using Calculus, and not the corresponding graph of f (x), how do you know where this
function is increasing/decreasing?
(2) What can be concluded when a function changes from increasing to decreasing or vice­versa?
(3) Using Calculus, how can we find those points and how can they be used to create a sketch of
the corresponding graph of f (x)?
and finally ...
(4) Why do you think that today's lesson should be titled quot;The First Derivative Testquot;?
I have placed a copy of this document in FC inside the Unit 2 Investigating Derivatives folder that
resides in the Course Content Area. I would like each school of students to discuss these
questions, collect your thoughts and then share them with your classmates by posting your
collaborative work as a public presentation at http://www.slideshare.com.
1

2. MCV4U ­ Curve Sketching Day 1
Consider the function f (x) = 2x3 ­ 9x2 ­ 108x + 2 and discuss the following
questions ...
(1) Using Calculus, and not the corresponding graph of f (x), how do you know where this
function is increasing/decreasing?
(2) What can be concluded when a function changes from increasing to decreasing or vice­versa
(3) Using Calculus, how can we find those points and how can they be used to create a sketch o
the corresponding graph of f (x)?
and finally ...
(4) Why do you think that today's lesson should be titled quot;The First Derivative Testquot;?
I have placed a copy of this document in FC inside the Unit 2 Investigating Derivatives folder th
resides in the Course Content Area. I would like each school of students to discuss these
questions, collect your thoughts and then share them with your classmates by posting your
collaborative work as a public presentation at http://www.slideshare.com.
2

3. (1) Using Calculus, and not the corresponding graph of f (x), how do you know where this function is
increasing/decreasing?
(2) What can be concluded when a function changes from increasing to decreasing or vice­versa?
(3) Using Calculus, how can we find those points and how can they be used to create a sketch of the
corresponding graph of f (x)?
3

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