MAT 151 Review for Test #3
Expect approximately nine questions. The basic rules for differentiation will be tested as will as knowledge of exponential and logarithmic functions and their applications.
One testing differentiation rules:
- Constant Rule, Simple Power Rule, Constant Multiple Rule, Sum and Difference Rules, Product Rule, Quotient Rule, General Power Rule.
- Derivatives of natural exponential functions, derivatives of exponential functions, derivatives of natural logarithmic functions, derivatives of exponential and logarithmic functions involving other bases.
One from chapter Two:
- Know how to work problems 43, 57, 61, 75 on p. 168.
One from chapter Three (The question will require knowledge of the function extrema and points of inflection as they apply to solving profit, cost and revenue problems.):
- Problems 50 and 53 on page 253 as well as example #5 on page 197 are good examples of the question from chapter 3. Remember that you must be able to solve the problem analytically and graphically. Use one method to verify the solution found by the other.
Six from chapter Four:
- Use the properties of exponents and logarithms to evaluate and simplify exponential and logarithmic expressions as in problems 5 - 12, 53 - 64 on pp 308 - 311. Then find the derivative.
- Be able to use the properties and derivatives of exponents, logarithms, and their functions to solve real life questions as in 91 - 97 on pp 308 - 311.
- Be familiar with the graphs of ax and ln (x). Be able to recognize translations, shifts and rotations of these graphs and to write equations incorporating these changes and graph them.
Bonus
- Know the definitions of a continuous function, when a function is differentiable, the limit definition of the derivative, and the limit definition of the number e. Expect a bonus question related to these definitions.
