Curve sketching is an important application of derivatives. Here’s an example with a polynomial, with pictures to help assist understanding:
Precalculus Resources: Spring 2017 Midterm II Review
I have gathered quizzes that relate directly to the upcoming midterm, as well as included a sample midterm. Please feel free to use these for practice! If you have trouble with the material, visit this page for additional resources. Don’t forget to grab a free version of wolfram alpha pro to help you if you’re enrolled at San Francisco State University!
- 2.4: Polynomials
- Vertex of a parabola
- Determine the behavior of a polynomial near or
- 2.5: Rational Functions
- Determine the behavior of rational functions near to
- Determine the vertical and horizontal asymptotes of a rational function
- Determine the holes of a rational function, if they exist.
- 3.1: Exponential and Logarithmic Functions
- Their definitions as inverses
- Practice using #23 – #32 in Precalculus – Prelude to Calculus, 3rd Ed.
- 3.2: Power Rule
- Change of Base
- 3.3: Product and Quotient Rule
- Read p.249-p.252 for applications in scientific settings
- 3.4: Exponential Growth
- Compound Interest (n times per year)
- 3.5: e and the Natural Logarithm
- Understanding the definition of e will enhance your understanding of proofs later on. For now, we know it’s a real number that is approximately equal to 2.71, and it’s associated with Continuous growth!
- 3.7: Exponential Growth Revisited
- Read p.304-p.306 for an application of the approximation methods discussed in 3.6 used in financial estimations.
- Focus on Continuous Compound Interest
- 4.1: Unit Circle
- 4.2: Radians
- Make sure you can convert between degrees and radians.
- 4.3: Sine and Cosine
- Definition using unit Circle
- Domain and Range of Sine & Cosine
- If you want a challenge, try answering #45 from this section.