How do I write this in maple?

Find the point on the parabola x + y 2 = 0 that is closest to the point (0, -3).

Thank you!

Graph the curve with equation y(y2 −1)(y − 2)= x(x −1)(x − 2)
At how many points does the curve have horizontal tangents?

Estimate the x-coordinates of these points.

Find the equations of the tangent lines at the points (0,1) and (0,2)

Find the exact x-coordinates of the points of these points.
Create even more fanciful curves by modifying the equation.

PLEASE WRITE STEP BY STEP IN MAPLE

How to get rid of the boundary

display(ellipse([0, 0], 2, 1, filled=true, color = red),size=[1000,500],axes=none);

or how to make the boundary the same color as the filled region?

I am trying to adapt the code with Direct Search 2 for my needs but do not quite understand the syntaxis :( . I have system with 8 first order but nonlinear odes and 20 parameters but for starters I fix most of them (to estimate time consumption for full calculations etc). The part of the code where it ``breaks'' looks as follows:

#argument
X0:=Vector([24, 36, 48, 60, 72, 84], datatype = float):
#value
Y0:=Vector([13.8e+9, 12.13333333e+9, 10.7e+9, 10.5e+9, 9.8e+9, 10.1e+9], datatype = float):

#so this is the data - time in X0 and corresponding observables (at that time instances) at Y0

par_sol:=dsolve(dsys, numeric, range=0..85,  parameters=[eta_L, L0]);

#parametric numerical solution with eta_L parameter of the model and L0 initial condition to fit

ffit2 := proc(etaLValue, L0Value, tValue) global old_eta, old_L0; local res;
if not [etaLValue, L0Value,tValue]::list(numeric) then
      return 'procname'(args); end if;
if old_eta<>etaLValue and old_L0<>L0Value then
      (old_eta,old_L0) := etaLValue,L0Value;
      par_sol('parameters'=[eta_L=etaLValue,L0=L0Value]);
   end if;
   res:=rhs(par_sol(tValue)[4]); end proc;

# this is just adapted copy of your function

par_sol(parameters=[eta_L=0.004, L0=1.1e10]);

par_sol(84)[4];ffit2(0.004, 1.1e10, 84);

#their output coincide OK; same for another trio of parameters

DS2:=CodeTools:-Usage(
        DirectSearch:-DataFit(ffit2,X0,Y0,t,
                              [ eta_L=0.001 .. 0.1, L0=1.5e10 .. 1.7e10
 #                               
                              ] )
);

#and here it breaks:

Warning, initial point [L0Value = .9, tValue = .9] does not satisfy the inequality constraints; trying to find a feasible initial point
Error, (in DirectSearch:-Search) cannot find feasible initial point; specify a new one

But tValue is a time variable - I integrate over it, it is not a parameter to fit - I evaluate ffit2 at it. So basically ffit2 return exactly the model value which need to be fited with data in Y0 at times specified in X0. I thought it is easier than the other problems I saw in examples with Direct Search 2 and still I can't get through syntax neither with it not with NonlinearFit of core Maple...

I would appreciate if you could point me what I am doing wrong. Just in case I also attach full version of the file.01test.mw

Thank you in advance!

Hello. I want to organize some parameter
F=fsolve(1+x^2=j).

If j=-5, for example, an empty value 'F=' will be returned. How can I write the expression

If F=(void), then action 1, else action 2 end if

The fact is that I just don't know how to write the result (void), that is, the result of 'F ='

Thanks

Hi

I was wondering how one uses maple to solve for variables that comprise the limits of an integral?

X and R are between 0 and 1.

Any thoughts would be greatly appreciated, thanks in advance...!

Download Solvingforlimitsofintegrals.mw

When should i use ->  for a procedure definition and when not ?
In my post i do see examples of  procedures which are made on two different ways.
proc  ..end proc;

Still difficult to get a procedure on two ways 

test:=x->x^2;
Typesetting:-mprintslash([(test := x -> x^2)],[x -> x^2])

test(2);
4

restart;
test:= proc()
local x,a;
a:= x^2;
end ;
Typesetting:-mprintslash([(test := proc () local x, a; a := x^2; end proc)],[
proc () local x, a; a := x^2; end proc])

test(2);
x^2

test(3);
x^2

As you can see with the standard proc definition i getlost with  calculating x^2 

In the past I worked with mathcad where it was very easy to work with units. Now I try to switch to Maple but I am still struggling when I want to implement units. In the simple attached worksheet I try to multiply vector a in [m] with vector b in [cm]. I get an answer in [m] but I cannot convert the answer to another unit. Right clicking allows me to change the unit e.g. to mm but nothing happens in the worksheet. When I use convert, the units are expressed numerical in cm but the vector still shows m. My apologies in advance for this simple questions but I find no way to solve my issue.

CollabExample.mw

Anyone can help me to convert matlab codes to maple, pls, this is my code p

Can i make a natural numberline what shows the enumber of primes at each of 1000 numbers  
I have her

0-1000 : 168
1000 -2000: 135

2000-3000 : 127

3000- 4000: 120

4000 -5000 : 119 

then a gap (jump) 

10^7- 1000- 10^7  : 53 

You can see that the "number of primes"  is fluctuating
Can i make a procedure what calculates the latest mersenne prime number ?
Problem is only that there is a theorem: there are arbitrary long series of divisible numbers on the numberline 
There are gaps of length n - 1, where are no primenumbers  in positioned.

The idea is to get a idea of the distribution of primes to make a guess from where to start to find another one? 

Hello, I found this code from Acer works great:

p=floating point number such as 0.003483 

nprintf(`#mn(\"%1.3e\");` , p)

prints a number in Scientific format,    3.483e-03

Perfect.

HOWEVER, What is the #mn please?   Is it a comment, or a MathML function?

Regards, Bill

Dear all, do you know if there is a way to ask Maple and the Physics package to use the bold notation of vectors instead of using arrows? 

Thanks, Kevin

Hi,

I want to solve system of  PDE equations by maple and i dont know how can i write it codes that can solve them for me. Can anyone help me please??!!