1. MCV4U Curve Sketching Day 2
Consider the graph of the function f(x) below:
3x^3 ­ 18x^2 ­ 72x + 192
Question 1: Sketch the first and second derivative of this function on the same set of axes as the original function f (x).
Question 3: Using the definition of f (x) above, verify your conclusions from the previous questions.
Question 4: Why do you think that today's lesson could be titled quot;The Second Derivative Testquot;?
Practice Questions ­ Page 350 # 7a, 7c, 8 and 9
You are to use the 2nd derivative test to classify each of the critical points that you find.
For # 8, create a sketch of f (x) using the first derivative f '(x) only as your guide.
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2. Consider the graph of the function f(x) below:
Question 1: Sketch the first and second derivative of this function on the same set of axes as the original function f (x).
Question 2: How could the second derivative be helpful in determining if a critical point of f (x) [ ie. where f '(x) = 0 ] corresponds to
a maximum, minimum or neither?
Question 3: Using the definition of f (x) above, verify your conclusions from the previous questions.
Question 4: Why do you think that today's lesson could be titled quot;The Second Derivative Testquot;?
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