MAT 1234 Calculus I

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);