2.1T 
Recognize and sketch tangent lines in various situations 
2.1V 
Estimate instantaneous velocity from average velocity by selecting
appropriate points 
2.2L 
Estimate limits and onesided limits graphically and numerically, and
also recognize when they do not exist 
2.3L 
Evaluate limits and onesided limits algebraically 
2.3C 
Determine at which points on its graph a function is discontinous and
describe the type of discontinuity 
2.4IVT 
Apply the Intermediate Value Theorem to show where
a root of an equation exists 
2.5L 
Recognize and evaluate limits of infinity or negative infinity
graphically, algebraically, and numerically 
2.5AS 
Use limits to determine where a function has a vertical or horizontal
asymptote 
2.6DI 
Interpret the derivative as the slope of the tangent line and as the
instantaneous rate of change 
2.6DC 
Calculate the derivative of simple algebraic
functions from the limit definition 
2.78R 
Recognize f, f', f'' from given graphs 
2.78SF 
Use the graph of f to sketch a graph of f' 
2.78D 
Determine where a function is differentiable graphically and
algebraically, and describe why it is not differentiable 
2.78SF 
Use the graph of f' to sketch a graph of f 

Classes of functions you should be able to analyze: algebraic
functions, circular and inverse circular functions, exponential and
logarithmic functions, and parametric functions

3.17B 
Memorize derivatives of the basic functions in each class 
3.17DR 
Differentiate sum, difference, product, quotient, and composition of
functions from these classes 
3.17LD 
Recognize and apply logarithmic differentiation when appropriate 
3.17ID 
Recognize and apply implicit differentiation when appropriate 
3.17T 
Determine where a curve has a horizontal or
vertical tangent (for explicit or implicit functions, and parametric
curves) 
3.17T 
Calculate the equation of the tangent line at a
point on a parametric curve or an implicit function 
3.8M 
Derive velocity and acceleration from the position function for an
object in motion 
3.8O 
Optional standards for other applications:
chemistry, biology, economics, etc. 
3.9L 
Calculate the tangent line approximation for a function and determine
whether it is an over or an underapproximation 
3.9D 
Use differentials to approximate change and
error 
4.1RR 
Model related rates as a mathematical equation and solve the problem
using calculus 
4.2MM 
Use calculus to determine the local and absolute extrema of a function
on a given interval 
4.3MVT 
Understand the consequences of the Mean Value Theorem graphically and
identify points on the graph whose existence satisfies the conclusion of the
MVT 
4.3G 
Use the functions f' and f'' to answer questions about the graph of
f 
4.5IF 
Recognize all indeterminate forms: 0/0, inf/inf, 0*inf, infinf, 1^inf,
inf^0, 0^0 
4.5LH 
Evaluate limits of the form 0/0 and inf/inf 
4.5LO 
Evaluate limits of the difference, product, and
exponential indeterminate forms 
4.6O 
Model a quantity to be optimized as a function of
one variable and solve the optimization problem 
4.7NA 
Apply Newton's Method to approximate zeros to a
given degree of accuracy 
4.7NF 
Recognize when Newton's Method fails to converge to
the desired zero 
4.8M 
Memorize the antiderivatives of basic functions 
4.8C 
Calculate families of antiderivatives and solutions of initial value
problems 
5.1RS 
Express areas as limits of Riemann sums, including the use of sigma
notation 
5.2DI 
Express and evaluate a definite integral as the
limit of a Riemann sum 
5.2RS 
Compute left, right, and midpoint approximations of definite integrals
and state (if possible) whether the approximations are over or
underestimates 
5.2P 
Use the properties of definite integrals to compute new integrals from
old integrals 
5.3ET 
Evaluate definite integrals using the Evaluation Theorem 
5.3EI 
Recognize and evaluate indefinite integrals 
5.3M 
Set up and evaluate integrals to find displacement and total distance
traveled from a velocity function 
5.4AF 
Sketch the graph of an "area under f" function from
a graph of f 
5.4FTC 
State both parts of the FTC and explain their
meaning and importance 
5.4D 
Use FTC (and chain rule) to find the derivative of area functions 
6.1A 
Set up integrals (with respect to x and y) representing the area between
two curves 
6.1P 
Set up integrals representing the area enclosed by parametric
curves 