Math 151 – Final Examination “Guide”
Exam is Thursday, May 6, 10:30 – 12:20
What’s on the Final - EVERYTHING WE HAVE COVERED STARTING WITH CHAPTER 7
Chapter 7: Trigonometric Models
I.
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Reading information from a graph or formula of f (x )  a sin bx  h  k
 amplitude
 period
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 average value
 phase shift
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II. Sketching the graph of f (x )  a sin bx  h  k
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III. Finding a model, from data, of the form f (x )  a sin bx  h  k using the calculator and
by hand
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Chapter 9: Multivariable (3-D) Functions
I.
Reading a 3-D Function
 from the 3-D graph
 from a table
 from a contour graph
II. Relationships Between 3-D Graph and Contour Graph
 be able to match a 3-d graph with its contour graph
III. Partial Derivatives
 be able to calculate first partials
 be able to interpret the meaning of first partial derivatives
 be able to make a second partials matrix (Hessian)
IV. Compensating for Change – finding and using

dy
dx
for a given 3-D function
Chapter 10: Multivariable (3-D) Optimization
I.
Critical Points
 be able to find and classify critical points from a contour graph (shaded, labeled, or
with an accompanying 3-D graph)
• be able to identify critical points from a table of data
II. Optimization
 be able to classify critical points using the determinant/Hessian test
III. Optimization Under Constraints
 be able to find max or min values of a 3-D function under the constraint g x, y  c
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 interpret the meaning of a LaGrange multiplier 
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How/What to Study
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Your primary source of study material would be quizzes 2 – 6
Next, review/do all assigned homework problems from chapters 7, 9 and 10
Finally, review all class examples for chapters 7, 9, 10
My Availability
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M: 9:00 – 3:00
T: 12:00 – 3:00
W: 9:00 – 3:00
Th: 9:00 – 10:00
I will most likely be in the tutoring lab (Hinkle 126) during these times, if not there then in my
office (Hinkle 131) or wandering the main hallway in Hinkle hall.