MAT 1234 Calculus I Section 3.5/ 3.6 Graphing with Maple

Homework No WebAssign HW Turn in the attached HW problem

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

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

Example 1 Open Maple and work along with the slides

Example 1

Domain

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

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

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

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

Vertical Asymptotes

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

Intervals of Increase and Decrease

Local max./min.

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

Intervals of Concavity

Inflection Points

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