## Help with local max/min problem...

*Find the cubic ax^3+bx^2+cx+d that has a local minimum at (‐1, ‐2) and a local maximum at (4, 4). Plot it.

How do i approach this problem?

## How to check if a property applies to all coprimes...

Hi, I'm rather new to Maple but I have to find a composite number n which has the property that all her coprimes a fulfill the expression "a^(n-1) - 1 mod n = 0". I already found out that such numbers are called Carmichael numbers. But of course I need to use Maple and the information I was given by our professor. My problem is that I have no idea how to check if "a^(n-1) - 1 mod n = 0" is true for all coprimes of a given n. How do I? ;) btw. I don't know if I used the correct vocabulary here, so please forgive me if I expressed something wrong.

## how to save solution from a solve?...

I have this problem

I have to solve something like this

for i to 17 do

solucion[i] := solve({item3[i], item4[i]}, {x, y})

end do

and I obtain in the answer for example

solucion[1] =             {x=2,y=3}

solucion[2] =             {x=3,y=4}

and I would like to create a vector containing all the values for x and all the values for y like x[1]=2  x[2]=3 and so on

## Can Anyone help me with this question?...

The position of a particle in space at any time t>=0 (in seconds) is given by x(t)=t^(3/2), y(t)=2t^(5/2), z(t)=t^2 (in meters). Use the connamds diff and fsolve to find the time t when the particle fisrt reach the speed of 300 m/s.

thank you!

## Differentiation...

If I have an expression which represents the following:

## computing ArcLength for space curve...

Not sure how to compute my question into maples. Tried various ways and nothing has worked yet. Need help, I am new with Maples. Here is the problem that I am trying to enter into maples:

find arc length of space curve:

r(t)= 2e i + ecos(t) j + esin(t) k, where t is > or = 0 and < or = to ln(3). r(t), i, j, and k all have vector arrows above them.

Can anyone give me a hint on how to enter this into maple?

## LambertW...

Dear all,

Im solving the following equation: V=I(t) * Z (V)

I substitute I and Z with the corresponding equations and I solve for V :

V:=solve(V=(1.027*exp(-t/0.282)+0.051*exp(1/t+(1.766*10^90))))*(2.433*10^3*exp(-0.008*V)+780),V):

and maple solves nicely  it using LambertW and i can plot V for a range of t.

I want to do the same but instead of the equations of I=f(t) and Z=f(V) to use straight the values from tables like:

## Eigenvector...

I have a matrix,  T:=[cos(x)  -sin(x); sin(x)  cos(x)].

Maple11 can calculate the eigenvalues symbolically. Nice property. However

(v,e):=Eigenvectors(T)

gives

Error, (in LinearAlgebra:-LA_Main:-Eigenvectors) expecting either Matrices of rationals, rational functions, radical functions, algebraic numbers, or algebraic functions, or Matrices of complex(numeric) values.

Is there any possibility to calculate the eigenvectors symbolically?

Thanks,

## finding my roots......

Hi everyone,

i want to find the solution(s) to the following equation numerically:

f:=1+x^2+1/100*abs(ln(3-4*x))=0;

But fsolve refuses to work, it just gives the input back. Setting Digits to a stellar value didn't help, i also tried different initial points.

Thomas

## Solving Augmented Matrix step by step...

As the subject says, how do i solve an augmented matrix step by step so i can follow each change in the matrix. The augmented matrix is two 3x3 matrixes put together with the operator (<A|B>]. I hope yoy understand my "Swedish English".

Kefil

## Weird partial derivative...

<p>Hey,</p>
<p>I've got this function:</p>
<p>f(x) = (x + y)(x^2 + y^2)</p>
<p> </p>
<p>By applying the product rule by hand I get the following partial derivative (with respect to x):</p>
<p>df/dx = (x^2 + y^2) + (x + y)2x</p>
<p> </p>
<p>I would expect Maple to give me the same result but instead I get the following:</p>
<p>f := (x + y)(x^2 + y^2)</p>
<p>diff(f,x) = 2*(D(x))(x^2 + y^2)*x + 2*(D(y))(x^2 + y^2)*x</p>
<p> </p>
<p>This has me a bit stumped so I'm hoping someone is able to help me out.</p>

## Importing Data in Maple...

I have a problem and hope, anybody can help me with that.

I have density data dependig on temperature and pressure. The data are stored in an excel file (in a square block - see attachment). Is there an easy way to import this data in Maple, that I can use several values of the density at given a pressure and temperature? Maybe comparable with a table (or matrix) where you can pick out indexed values, e.g. rho[temperature,pressure].

My current solution is to write a procedure, but before that I would like to know if there is an easyer way.

## changing fonts in a legend...

How can I change the fonts used to create the legend for a plot?

What I really want to do is increase the font size. I can do this for the title, labels, and axes - but not for the legend. (At least I don't see how to do this in the online help.)

Before I start digging through the code, I thought I'd see if anyone here has dealt with this previously.

Doug