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MAT 1234 Calculus I

This resource provides a comprehensive guide for graphing functions using Maple software in Calculus I, specifically focusing on sections 3.5 and 3.6. It covers key aspects like domain, intercepts, asymptotes, and intervals of increasing/decreasing behavior. Users will learn to detect local maxima/minima, intervals of concavity, and inflection points. The practical application involves plotting a polynomial function, analyzing critical points, and adjusting graphs to reveal essential information. This is an essential tool for visualizing and understanding calculus concepts through software.

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MAT 1234 Calculus I

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  1. MAT 1234Calculus I Section 3.5/ 3.6 Graphing with Maple http://myhome.spu.edu/lauw

  2. Homework • No WebAssign HW • Turn in the attached HW problem

  3. Preview • In practice, we use software to produce graphs • Try to make sure all important information are revealed • Software limitations

  4. Important Information • Domain • Intercepts • Vertical/ Horizontal Asymptotes • Intervals of Increasing / Decreasing • Local max./ min. • Interval of Concavity • Inflection Points

  5. Example 1 • Open Maple and work along with the slides

  6. Example 1

  7. Domain

  8. First Plot >f:=x->2*x^6+3*x^5+3*x^3-2*x^2; >plot(f(x),x=-5..5);

  9. x-intercepts >fsolve(f(x)=0); x-intercepts:

  10. y-intercepts >f(0); y-intercepts:

  11. Horizontal Asymptotes >limit(f(x),x=-infinity); >limit(f(x),x=infinity);

  12. Vertical Asymptotes

  13. Intervals of Increase and Decrease > >fprime:=D(f); >fsolve(fprime(x)=0);

  14. Intervals of Increase and Decrease

  15. Local max./min.

  16. Intervals of Concavity > >fpp:=D(fprime); >fsolve(fpp(x)=0);

  17. Intervals of Concavity

  18. Inflection Points

  19. Adjusted graph >plot(f(x),x=-3..1,y=-16..1);

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