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Applied Calc Help using Maple 12

Posted on 2008-07-15 22:10 By ptroubador (8)
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How do I enter this problem in Maple 12? I have a few like this and need to knwo how to input the equations.

1.)  Find the slope of the tangent line to the curve y=x^3+3x-8 at (2,6)

2.) The tangent line to the circle y=x^3 -6x^2 -34x -9 has slope 2 at two points on the curve. Find the two points.

3.)Find the slope of the curve y=x^5 at x= -2

‹ 2nd Derivative problem with Maple 12 Student Edition assistance ›
alec's picture

student package

Comment on 2008-07-15 22:43 from alec (Maple Rating 4 1443)

It is easy to do using deprecated student package,

with(student):
eval(slope(y=x^3+3*x-8),x=2);

                                  15

y:=x->x^3 -6*x^2 -34*x -9:
map(x->[x,y(x)],[solve](slope(y(x))=2))[];

                         [6, -213], [-2, 27]

eval(slope(x^5),x=-2);

                                  80

Note that the curve in b) is not a circle.

Alec

commands questoin

Comment on 2008-07-15 23:03 from ptroubador (8)

 
 
 
 
As I am relatively new to Maple, I barely used Maple 11 before 12 came out, so I am still in the learning phase of the commands, so bear with me. In problem 1 I did the eval, but I came up with the slope of y=6. Is there a syntax that I forgot to put? Maybe there is one step I missed, as I noticed that yuour response equation was different than the equation I wrote. Thanks Again for your help.
 
 
P.Miller

alec's picture

Where is the difference?

Comment on 2008-07-15 23:08 from alec (Maple Rating 4 1443)

Where is the difference? You wrote y=x^3+3x-8  and I wrote y=x^3+3x-8.

At x=2, for y defined like that, y=6. It doesn't have to be entered.

Alec

  Please explain your

Comment on 2008-07-15 23:24 from ptroubador (8)

 
 
Please explain your second sentence in Maple terms so I understand Maple. Do I have to plug the answer in the orig eq to get my answer? After I am entering my equation, I am using control =. Is this right command or do I use right click? I made the command on problem 2, and I came up with -32. Where am I going wrong, perhaps I am not reading your answer in Maple terms. 
 
P.Miller

alec's picture

I give up

Comment on 2008-07-15 23:39 from alec (Maple Rating 4 1443)

I think, we have some communication problem. I hope that somebody else will help you. I give up. 

Alec

Doug Meade's picture

solution using calculus

Comment on 2008-07-16 13:55 from Doug Meade (Maple Rating 4 617)

You are a student learning calculus. Let's keep the focus on calculus and make use of basic Maple commands (not specialized commands that completely avoid the relevant mathematics).

Here is how I would use Maple to answer each of your three questions:

1.)  Find the slope of the tangent line to the curve y=x^3+3x-8 at (2,6)

F1 :=x^3+3*x-8;
                                 3          
                                x  + 3 x - 8
dF1 := diff( F1, x );
                                     2    
                                  3 x  + 3
m1 := eval( dF1, x=2 );
                                     15

2.) The tangent line to the circle y=x^3 -6x^2 -34x -9 has slope 2 at two points on the curve. Find the two points.

F2 := x^3-6*x^2-34*x-9;
                             3      2           
                            x  - 6 x  - 34 x - 9
dF2 := diff( F2, x );
                                 2            
                              3 x  - 12 x - 34
solve( dF2=2, x );
                                    6, -2
p1 := eval( [x,F2], x=6 );
                                  [6, -213]
p2 := eval( [x,F2], x=-2 );
                                  [-2, 27]

3.)Find the slope of the curve y=x^5 at x= -2

F3 := x^5;
                                      5
                                     x 
dF3 := diff( F3, x );
                                       4
                                    5 x 
m3 := eval( dF3, x=-2 );
                                     80

Notice that I answered these questions using only three basic Maple commands: diff, eval, and solve. No extra packages and no fancy optional arguments.

I hope this is helpful,

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed
Tim Vrablik's picture

Visuals

Comment on 2008-07-16 10:53 from Tim Vrablik (Maple Rating 1 48)

The error you might have been making in the first example is you might have forgot to put in 'slope' inside the brackets.  The function was being evaluated at 2, which would give you an answer of 6

Here is a bit more of a visual way of getting your answers for 1 & 3:

with(Student[Calculus]):
Tangent(x^3+3x-8, x=2, output=slope)
Tangent(x^5, y=-2, output=slope)
 

You can change output to line to get the equation of the tangent, or plot to see the tangent and the function plotted together.

lemelinm's picture

Here is how I would do it

Comment on 2008-07-16 11:09 from lemelinm (Maple Rating 2 164)

Hi,

For 1)

> y := (x) ->  x^3+3*x-8; # this is an arrow procedure.

                                      3          
                           y := x -> x  + 3 x - 8
> y(a);

                                 3          
                                a  + 3 a - 8
> with(Student[Calculus1]);

> Tangent(x^3+3*x-82, x = 2, output = slope);

                                     15
> y(2);

                                      6

Then for 2)

> y := (x)  -> x^3-6*x^2-34*x-9

                                  3      2          
                       y := x -> x  - 6 x  - 34 x - 9
> Tangent(y(x), x = x, output = slope);

                                 2           
                              3 x  - 12 x - 34
> sol := solve(% = 2, x);  #wher % mean the last output

                                sol := 6, -2
> y(6);

                                    -213
> y(-2);

                                     27

then for 3)

> y := (x) -> x^5 

                                           5
                                y := x -> x 
> Tangent(y(x), x = -2, output = slope);

                                     80

Hoping this will help.  Of course, I hope that you understand the theory before letting Maple does the calculation.  It's YOUR responsability!

 

 I appreciate the

Comment on 2008-07-16 19:41 from ptroubador (8)

 I appreciate the responses. Of course doing it by hand is what the Professor originally had us do lasst semester, this semester there is so much work and taking a full load behooved me to use some software  rather than the 89 for calculations, the eye strain from the screen was too much. I need to learn more about the commands. As I have said earlier, this is my 1st math software I have used, and translating the problem from paper to Maple is a challenge for me to be ablt to check my answers. Maybe this software is too much, or I am trying to read too much into the answers provided hereto. If I understand correctly, I enter in to Maple exactly as is written  or do I use the clickable math. I know that once I understand how to enter problems into Maple then I will pick up quickly and understand how Maple works and what inputs and how to input the data. So, if there is some specific way for someone to walk me through 1 of the problems, I can more than likely understand what I am doing wrong.
Paul

Doug Meade's picture

typing vs clickable

Comment on 2008-07-16 22:35 from Doug Meade (Maple Rating 4 617)

If you want to utilize the commands from the student or Student'Calculus1] packages, you are going to have to type them out - or rely upon command completion. If you want to use the basic commands (diff, eval, and solve) then you have some options. For diff and eval, you can use the palettes (clickable). You can probably use the context menus to access solve, but only after you explicitly construct the equation that you want to solve. You have some flexibility in how you actually enter the commands. Personally, I find it fastest to simply type the commands (and use command completion for the commands with longer names).

Doug

---------------------------------------------------------------------
Douglas B. Meade  <><
Math, USC, Columbia, SC 29208  E-mail: mailto:meade@math.sc.edu       
Phone:  (803) 777-6183         URL:    http://www.math.sc.ed
lemelinm's picture

What I am suggesting

Comment on 2008-07-17 10:21 from lemelinm (Maple Rating 2 164)

 HI Paul,

One way to learn about Maple is to go in the menu, choose help -> take a tour of Maple.  You will learn a lot about Maple.  As for working with clickable math,  you will need to enter your functions and equations by hand firts before doing anything with the mouse.  Like Doug suggest, learning to write the command will help you to better understand what's happening when you click.  Step by step, it's the only way and it's not only for Maple but to any new software.  If you have others questions, don't hesitate.  MaplePrimes is there for that.

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