Chapter 6 Review
New Concepts
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Implicit Differentiation
Mean Value Theorem for Integrals
Mean Value Theorem for Derivatives
Improper Integrals
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Distance/Velocity/Acceleration Functions
○ Determine initial values
○ Determine height at any time
Optimization
○ Use math language when solving
○ Apply either 1st or 2nd derivative test
Finding Derivatives (Rules)
○ Power
○ Product
○ Quotient
○ Chain
○ Trig
○ Combine all rules together :-)
FTC - Chain Rule Extension
○ Review FTC for derivative or integral
and integral of derivative
Applying L’Hopital’s Rule
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Review Concepts
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Distance v Time graphs and Velocity v Time
Evaluate limits
Define Continuity using limits
Define Differentiability using limits
Definition of Derivative
Compare f(x), f’(x), f”(x). Use derivatives to
describe a function (using increasing,
decreasing, max, min and concavity)
Integral “Rules” and properties for writing as
a single integral
Translating integrals
○ +k adds a rectangle
○ -h must shift bounds with equation
Fundamental Theorem of Calculus
○ Part 2 F(b)-F(a)
○ Part 1 derivative of integral & integral
of derivative (Definite and Indefinite)
Area between two curves
○ Vertical
○ Horizontal