MAT 1234Calculus I

Section 3.5/ 3.6

Graphing with Maple

http://myhome.spu.edu/lauw

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

6 5 3 2( ) 2 3 3 2f x x x x x

Domain6 5 3 2( ) 2 3 3 2f x x x x x

?Domain

First Plot6 5 3 2( ) 2 3 3 2f x x x x x

>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);

lim ( ) ? lim ( ) ?x x

f x f x

Vertical Asymptotes

Intervals of Increase and Decrease

>

>fprime:=D(f);

> fsolve(fprime(x)=0);

( ) 0f x

Intervals of Increase and Decrease( ) 0f x

Local max./min.

Intervals of Concavity

>

>fpp:=D(fprime);

>fsolve(fpp(x)=0);

( ) 0f x

Intervals of Concavity ( ) 0f x

Inflection Points

Adjusted graph

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