FINAL EXAM REVIEW SHEET
General Knowledge: Again, all your Pre-Calc concepts are fair game, which
include, but not limited to: factoring, graph translations, geometric formulas (both
2D and 3D), graphs of basic functions, Pythagorean Theorem, distance formula, etc.
Theorems/Definitions: While I might not explicitly have you state these, keep in
mind that they do show up as true/false questions.
Continuity (at a point, on a closed interval) (p. 105)
Intermediate Value Theorem (p. 111)
Definition of Derivative (p. 125)
Extreme Value Theorem (p. 239)
Critical Point (p. 241)
Rolle’s Theorem (p. 245)
Mean Value Theorem (p. 247)
Inflection Point (p. 261)
Test 1 Concepts:
Limits (Rational Functions, Trig). You may use L’Hopital’s Rule when it
applies. Remember the nonzero/zero rule.
Asymptotes (Horizontal, Vertical, Slant)
Continuity: A lot of theorems require explanation of continuity; make sure
you are able to do so.
Piecewise functions. You won’t have to draw them on the final, but you will
need to be able to analyze.
Tangent Lines, Average Rate of Change, Instantaneous Rate of Change
Definition of Derivative Computational Tricks: common denominators,
conjugate trick, factoring
Test 2 Concepts:
Derivative Rules: Sum, Product, Reciprocal, Quotient Rule. You will not have
to prove any of these, just be able to apply.
Trig and Arctrig Derivatives.
Exponential and Logarithmic Derivatives
Chain Rule
Kinematics: Acceleration/Velocity/Position both for Horizontal and Vertical
motion.
Implicit Differentiation
Logarithmic Differentiation
Related Rates.
Test 3 Concepts:
L’Hopital’s Rule
Local/Global Minimum and Maximum on a closed interval.
Extreme Value Theorem: Computing absolute extrema of f(x) on [a,b].
Increasing/Decreasing intervals and First Derivative Test on Critical Points.
Inflection Points and Concavity
Curve Sketching
Optimization: You will only be setting up optimization problems for your
final.
Test 4 Concepts:
Sigma Notation: Properties of sums, computing sums. You will not have to
come up with the Sigma Notation formula, but you should be able to sum
them up. The formulas previously given will still be supplied as needed.
Rolle’s Theorem and Mean Value Theorem: You will not be asked to solve for
c, just be able to determine if the theorem applies for the given situation.
Antiderivatives and Indefinite Integrals: Reverse Power Rule, Reverse Trig
properties, etc. Don’t forget the +c.
Initial Value Problems: Given f’(x), and given additional information, be able
to solve for f(x).
Kinematics Revisited: Acceleration, Position, Velocity for both horizontal and
vertical motion.
Integration using u-substitution.
Partitions, Left and Right Riemann Sums.
Area under a curve using Geometry.
Total Area
Definite Integrals
Integrable functions
Fundamental Theorem of Calculus I: The existence of integrals for
continuous functions. Also be able to use FToC I with the chain rule to
compute derivatives.
Fundamental Theorem of Calculus II: The evaluation theorem for Definite
Integrals.
Good Luck!