mat 1234 calculus i section 3.5/ 3.6 graphing with maple
TRANSCRIPT
![Page 1: MAT 1234 Calculus I Section 3.5/ 3.6 Graphing with Maple](https://reader035.vdocuments.mx/reader035/viewer/2022080917/56649efe5503460f94c1229b/html5/thumbnails/1.jpg)
MAT 1234Calculus I
Section 3.5/ 3.6
Graphing with Maple
http://myhome.spu.edu/lauw
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Homework
No WebAssign HW Turn in the attached HW problem
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Preview
In practice, we use software to produce graphs
Try to make sure all important information are revealed
Software limitations
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Important Information
Domain Intercepts Vertical/ Horizontal Asymptotes Intervals of Increasing / Decreasing Local max./ min. Interval of Concavity Inflection Points
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Example 1
Open Maple and work along with the slides
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Example 1
6 5 3 2( ) 2 3 3 2f x x x x x
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Domain6 5 3 2( ) 2 3 3 2f x x x x x
?Domain
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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);
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x-intercepts
>fsolve(f(x)=0);
x-intercepts:
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y-intercepts
>f(0);
y-intercepts:
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Horizontal Asymptotes
>limit(f(x),x=-infinity);
>limit(f(x),x=infinity);
lim ( ) ? lim ( ) ?x x
f x f x
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Vertical Asymptotes
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Intervals of Increase and Decrease
>
>fprime:=D(f);
> fsolve(fprime(x)=0);
( ) 0f x
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Intervals of Increase and Decrease( ) 0f x
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Local max./min.
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Intervals of Concavity
>
>fpp:=D(fprime);
>fsolve(fpp(x)=0);
( ) 0f x
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Intervals of Concavity ( ) 0f x
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Inflection Points
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Adjusted graph
>plot(f(x),x=-3..1,y=-16..1);