Math 118 - Intro to Quantitative Analysis II
Study Guide - Quiz #2

1. Write the formal definition of derivative i.e. that on p. 651, or Definition 1 on top of Lecture Notes #5.
2. Use this definition, sometimes called the limit definition of derivative (what might be called the "hard way"), develop the formula for the derivative of a function such as f(x) = 3x². You should know what the answer should be from doing it the short way, but you need to demonstrate why the answer is true.  You get NO CREDIT for just writing f '(x) = 6x.
3. Using the exponent rule, solve problems like those found in the On-Line Practice Problems under the headings "Polynomial Derivatives" and "Rational Exponents."
4. Using the product rule (d(hi^.ho) = ho^.d(hi) + hi^.d(ho)) and quotient rule (d(hi/ho) = (ho^.d(hi) - hi^.d(ho))/(ho^.ho)) solve problems like those found in the On-Line RUReady Problems under the headings "Derivatives of Products" and "Derivatives of Quotients."
5. For a given function, find the equation of the tangent line to the curve at some point (Problems like the On-Line RUReady problems under the section "Tangent Line Equations".)
6. Using the Chain Rule, solve problems like those found on the On-Line RUReady problems under the heading "Derivatives of Powers."