Mathematics Ma Study Guide - Midterm Guide: Quotient Rule, Power Rule

• School: Harvard University
• Department: Mathematics
• Course: Mathematics Ma
• Professor: Kelly

Document Summary

We solidified the concept of continuity in functions. In order for a function to be continuous, it must have a limit at all points, meaning that from the left and right, the functions are the same value. We can test this with piece-wise functions to make sure that at every point, the left and right hand sides are equal. We reinforced and introduced using derivatives as a method to find the rate of change of a function. In doing so, we established the following set of derivative rules. The power rule states that for a function raised to an exponent, you can multiply the function by the exponent"s value and raise it to the initial exponent"s value minus one. The constant rule states that you can find the derivative of a function being multiplied by a constant by multiplying the function"s derivative by the constant"s value. The latter two are a bit more difficult.