Math 180 C

Spring 2010

Exam 3 Review

Disclaimer: I have attempted to be comprehensive in the following, but important items may have been omitted by mistake. If you see such an omission, please let me know, but you are responsible for all of the lecture material to date.

The third hour exam for Math 180 will be held on Friday, April 9, and will cover section 3.5  through section 4.4  of the textbook.  In particular, be prepared to:

• Be able to use the chain rule.
• Be able to work with inverse trigonometric functions.
• Be able to take the derivatives of inverse trigonometric functions.
• Be able do define the basic hyperbolic functions (sinh, cosh, tanh) and take derivatives of them.
• Be able to calculate tangent and normal lines (again), including their application to implicit differentiation.
• Be able to give linear approximations to functions and to estimate values.
• Be able to solve rate of change problems, including "word problems".
• Use implicit differentiation, including (but not limited to), the calculation of functions implicitly defined by an equation, the calculation of inverse functions (including the inverse trigonometric functions), and the use of logarithmic differentiation.
• Be able to state (with preconditions), explain, and apply the Extreme Value Theorem.
• Be able to state (with preconditions, explain, and apply Rolle's Theorem and the Mean Value Theorem.  Statements of all theorems must be precise and include the requirements (preconditions) for the theorem to be true.
• Be able to state the corollaries to the mean value theorem and apply them to simple problems (including graphing and to differential equations (problems 27 - 35 on page 252 would be a good review for this part)).
• Be able to discover (using first and second derivatives) where a function is
• increasing or decreasing
• concave up or down
• has a maximum or minimum
• has a point of inflection

Any questions? Please ask!