4.5 Curve Sketching Name: In This Activity We Practice The 8-Step Process For Curve Sketching From Stewart's Calculus Book. A. Domain E. Intervals Of Increase Or Decrease B. Intercepts F. Local Maximum And Minimum Locations, Values C. Symmetry: Even, Odd, Neither G. Concavity Intervals And Points Of Inflection D. Asymptotes And Limits As X + 100 H. Sketch

 

4.5 Curve sketching Name: In this activity we practice the 8-step process for curve sketching from Stewart's Calculus book. A. Domain B. Intercepts C. Symmetry: even, odd, neither D. Asymptotes and limits as x o E. Intervals of increase or decrease F. Local maximum and minimum locations, values G. Concavity intervals and points of inflection H. Sketch the curve Follow the process, make your sketch, and only then use a graphing program to check your work. 1. Let f(x) = x-12x + 45x-34. Follow the process. A. Domain: B. It's good to plug in x = 0 and find the y value. But with a cubic function, it can be very hard to find the x intercepts. There is only one, at x=1. Just verify that f(1) = 0. c. f(x)=(-x)3-12(-x) + 45(-x)-34. Simplify and compare to f(x). Does it equal f(x)? -f(x)? If you can't tell, compare f(1) and f(-1). D. lim f(x) = lim x (1-+-- lim f(x)= x-400 E. Take the derivative. Are there x values where f'(x) does not exist? Increasing/decreasing can change there. Set f'(x) equal to zero to find the start and end of each interval of increase or decrease. F. G. Take the second derivative. Are there x values where f'(x) does not exist? Concavity can change there. Set f"(x) equal to zero to find the start and end of each interval of concavity. Places where f"(x)=0 may or may not be points of inflection. H. Choose the range of x values and y values that you need on your axes to show the intercepts and the critical points, draw and label perpendicular axes using straight lines, label values on the axes, then sketch the curve, label points of inflection and draw symbols for concavity. Now that you know increasing/decreasing and local minima, you can be sure that x = 1 is the only x intercept.