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A Summary of Curve Sketching Lesson 4.6 How It Was Done BC (Before Calculators) • How can knowledge of a function and it's derivative help graph the function? Regis might be calling for this information! • How much can you tell about the graph of a function without using your calculator's graphing? Algorithm for Curve Sketching • Determine domain, range of the function • Determine critical points Places where f ‘(x) = 0 • Plot these points on f(x) • Use second derivative f’’(x) = 0 Determine concavity, inflection points • Use x = 0 (y intercept) • Find f(x) = 0 (x intercepts) • Sketch Recall … Rational Functions an x n ... m bm x ... • Leading terms dominate m = n => limit = an/bm m > n => limit = 0 m < n => asymptote linear diagonal or higher power polynomial Finding Other Asymptotes • Use PropFrac to get r y m( x) b d ( x) • If power of numerator is larger by two result of PropFrac is quadratic asymptote is a parabola Example • Consider • Propfrac gives x 2x 7x 3 2 x 5 x 3x 3 5 4 Example • Note the parabolic asymptote Other Kinds of Functions • Logistic functions • Radical functions • Trig functions 10 h( x ) 2 3e x / 2 y x 16 x 2 1 f ( x) cos x cos 2 x 2 Assignment • Lesson 4.6 • Page 255 • Exercises 1 – 61 EOO