2311lectureoutline4.5 - positive and decreases where its...

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MAC2311, Calculus I 4.5 Summary of Curve Sketching When sketching the graph of a function f(x), consider each of the following: 1. domain (For what set of x values is f(x) defined?) 2. x and y intercepts (Let x = 0 to find y-intercept, let y =0 to find x-intercept(s) (label all intercepts on the graph) 3. symmetry (If f(-x) = f(x), then f(x) is symmetric about the y-axis. If f(-x) = -f(x), then the function has origin symmetry.) 4. vertical, horizontal and slant asymptotes (Set denominator = 0 to find vertical asymptotes. Find limits at infinity to determine any horizontal asymptotes. Slant asymptotes occur when a rational function has one degree higher in the numerator than in the denominator, and their equations can be found by dividing the numerator by the denominator. (draw and label any asymptotes on the graph) 5. intervals of increase or decrease (function increases where derivative is
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Unformatted text preview: positive and decreases where its derivative is negative) 6. local maximum and minimum values (set derivative = 0 or undefined to find critical numbers; any extreme values have to occur at the critical numbers) (label all extrema on the graph) 7. concavity (function is concave up when 2 nd derivative is positive and concave down when 2 nd derivative is negative) 8. points of inflection (inflection points occur where the concavity changes; set 2 nd derivative = 0 or undefined to find possible points of inflection) (label inflection points on the graph) 9. Sketch the graph using the above info. Use your graphing calculator to confirm your sketch. It is sometimes helpful to graph the function using technology first, so you have some idea where you are headed. Try exercises 2, 10, 14, 24, 38, 42 on page 314 in your text....
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This note was uploaded on 12/12/2011 for the course MAC 2311 taught by Professor Teague during the Spring '11 term at Santa Fe College.

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