Extrema on an Interval
Understand the definitions of extrema of a function on
an interval and relative extrema on an open interval.
Find extrema on a closed interval.
How do extrema relate to derivatives? What
Objectives: Use sigma notation to write and evaluate a
Essential Questions: What does sigma notation
In other words, a sigma gives you information to find the sum of
certain terms starting at one
Objectives: Distinguish between functions written in
implicit form and explicit forms. Use implicit
differentiation to find the derivative of a function.
Essential Questions: When would implicit differentiation
be most helpful
Unit 3: Concavity &
Second Derivative Test
Objectives: Determine the intervals on which a function
is concave upward or concave downward. Find any
points of inflection of the graph of a function. Apply the
Second Derivative Test to find relative extrem
Objectives: Solve applied minimum and maximum
Essential Questions: What does the First Derivative Test
have to do with Optimization? Does the process of
finding minimums and maximums change for application
Use your understanding of the Chain Rule and Implicit
Differentiation to find a Related Rate. Demonstrate your
understanding of Related Rates by solving real-life
problems, including those in AP format.
Objectives: Find a higher order derivative of a function.
Understand the relationship between position, velocity,
Essential Questions: How does a higher order derivative
help with our understanding of Physics
Objectives: Find the derivative of a function using the
Product Rule and Quotient Rule. Find the derivative of
a trigonometric function.
Essential Questions: Can derivative rules be combined
to solve a complex derivative?
Lines in the Plane
Objec&ves: Find the slope of a line and write linear
equa&ons for that line. Decide whether a rela&on
between two variables represents a func&on and nd
the domain. Evaluate dierence
Radians, Degrees, &
the Unit Circle
Objectives: Use radian and degree measure for angles,
and be able to convert between them. Use angles to
model and solve real-life problems. Evaluate
trigonometric functions using the unit circle. Use
Rolles Theorem &
Mean Value Theorem
Understand and use Rolles Theorem and the Mean
What are the similarities and differences between
Rolles Theorem and Mean Value Theorem? When
does each apply?
Objectives: Evaluate a definite integral using limits.
Evaluate a definite integral using the properties of
Essential Questions: How do definite integrals relate to
area under a curve? Explain the relation