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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? How much can you tell about the graph of a function without using your calculator's graphing?.
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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? • How much can you tell about the graph of a function without using your calculator's graphing? Regis might be calling for this information!
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 • 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 • If power of numerator is larger by two • result of PropFrac is quadratic • asymptote is a parabola
Example • Consider • Propfrac gives
Example • Note the parabolic asymptote
Other Kinds of Functions • Logistic functions • Radical functions • Trig functions
Assignment • Lesson 4.6 • Page 255 • Exercises 1 – 61 EOO
