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  1. Math 242: Calculus 1/
  2. Chapter 3/

Section 3.5

Summary of Curve Sketching

The examples in this section use everything we’ve learned for the previous four sections all at once. As a result, each video is quite long. Pause when you need to and ask any questions that you have!

Curve Sketching Guidelines #

Guidelines: A Sketching Checklist (and they really are guidelines, not hard rules)

  1. Find domain
  2. Find intercepts
  3. Does the function have symmetry? (Even / odd / periodic?)
  4. Find asymptotes: vertical and horizontal
  5. Find intervals of increasing and decreasing
  6. Find local maximum and minimum values
  7. Find concavity and points of inflection
  8. Sketch the curve.

Example #

Sketch $$ f(x) = \dfrac{2x^2}{x^2-1} $$

Example #

Sketch the graph of $$ y = \sqrt[3]{x^2-1} $$