Calculus
Lesson
17 Curve Sketching
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Curve Sketching: Things to do:
1) find intercepts
2) find relative extrema/points of inflection
3) find asymptotes
4) find concavities
5) check continuity
6) find domain and range
7) check symmetry
8) check differentiability
Note that not all of them are necessary each time! For instance, we can't solve
x^3 - x - 1=0 without a calculator. We also might not need 5-8 if we can figure
everything else out!
Examples:
Note: careful of 0/0 in h(x). Make sure to check for asmptotes in h(x).