mat 1234 calculus i section 3.5/ 3.6 graphing with maple
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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);
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