Functions 1 (F1).
I can compute limits of functions.
Section 4 Standards
Subsection 4.1 Functions (F)
Functions 2 (F2).
I can identify whether a function has any of the following asymptotes:
- Horizontal
- Vertical
- Oblique
Functions 3 (F3).
I can determine whether a function is continuous at a point.
Subsection 4.2 Derivatives (D)
Derivatives 1 (D1).
I can compute the derivative of a function using the limit definition.
Derivatives 2 (D2).
I can compute the derivative of a function using
- the power rule,
- the sum/difference rule, and
- the constant multiple rule.
Derivatives 3 (D3).
I can compute the derivative of a product or quotient of two or more functions.
Derivatives 4 (D4).
I can compute the derivative of a composition of two or more functions.
Derivatives 5 (D5).
I can use implicit differentiation to solve related rates problems.
Derivatives 6 (D6).
I can compute the derivative of transcendental functions and their inverses.
Subsection 4.3 Applications of the Derivative (A)
Applications of the Derivative 1 (A1).
I can use the first and second derivatives of a function to
- find the critical numbers,
- identify local extreme values,
- identify the concavity of a function on an interval, and
- identify inflection points.
Applications of the Derivative 2 (A2).
I can use the information from Functions 2 (F2) and Applications of the Derivative 1 (A1) to sketch the graph of a function.
Applications of the Derivative 3 (A3).
I can use the closed interval method to solve optimization problems.
Subsection 4.4 Integration (I)
Integration 1 (I1).
I can use the definition to compute the definite integral of a continuous function.
Integration 2 (I2).
I can use the Fundamental Theorem of Calculus to compute definite and indefinite integrals.
Integration 3 (I3).
I can use substitution to evaluate definite and indefinite integrals.
