Section 2.4

• Know what the theorems of this section state and their significance.
• Understand Examples 1, 2, and 5.
• Know the derivatives of the six basic trig functions. (You can derive the other four from the formulas for the derivatives of sine and cosine.)

• Understand the Chain Rule and the notation that goes along with it, and understand how to use it, including its repeated use.
• Learn the "Outside-Inside" rule on page 156.

• Understand how to compute derivatives by implicit differentiation.
• Know how to use implicit differentiation to compute slopes, tangents, and normals to curves.
• Know how to use implicit differentiation to compute higher derivatives.
• Understand the Power Rule for rational powers and how to use it.

• Understand and be able to use the strategy described on page 174.
• Understand the examples.
• Know the formulas for (i) the areas and perimeters of triangles, rectangles, and circles and (ii) volumes and surface areas for cubes, spheres, and right circular cylinders.

• Make sure you clearly understand the definitions of absolute (global) and local extreme values (maximum and minimum) and critical points.
• Know the Max-Min and First Derivative Theorems. Remember to check endpoints! Note that not every critical point is necessarily a local maximum or local minimum (see Example 5, page 194).
• Know how to compute absolute extreme values of functions on closed intervals.

• Understand Rolle's and the Mean Value Theorems and the three important corollaries. You are responsible for the statement and meaning of these theorems, but not their proofs.
• Be able to apply these theorems and corollaries: be able to find a function from knowing its derivative, including being able to find velocity and position from knowing acceleration, and know how to determine where a function is increasing or decreasing.

• Be able to apply the First Derivative Test for local extreme values.
• Understand the examples. Use the sign pattern of f'(x) over intervals to determine where f(x) is increasing and decreasing.

• Know the definitions of concave up, concave down, point of inflection, and cusps. Note that not all points where f''(x) is either zero or does not exist are necessarily inflection points (see Example 5, page 212).
• Know and be able to apply the two Second Derivative Tests, one for concavity and one for local extreme values.
• Use the sign pattern of f'' to determine where f(x) is concave up or concave down.
• Be able to graph a function using its first and second derivatives as described by the strategy outlined on page 214.

• Know the definitions of the limit as x approaches plus or minus infinity and the properties in Theorem 6.
• Understand how to take limits of rational functions as x approaches plus or minus infinity; remember while you study this that it is best to think in terms of 1/x.
• Know the definitions of horizontal, vertical, and oblique asymptotes and how to compute them.
• Be able to graph a function using its asymptotes and dominant terms.

• You need not remember the specifics of any of the examples or theorems in this section, but you should be able to do similar problems using the strategy described on page 236.

• Know the definitions of linearization and differentials.
• Be able to compute the linearization of a function.
• Understand the relationship between derivatives and differentials and how to estimate absolute, relative, and percentage change using differentials.

• Understand Newton's method: know the formula and the geometric interpretation, and be able to apply it.
• Skip the last three subsections on convergence, things that go wrong, and chaos.