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Question: How to find the points indicated in the graph of Heart equation?

Question:How to find the points indicated in the graph of Heart equation?

herclau 1038 Maple
derivative critical-points hessian
December 03 2017
0

Hello,
How to find the points indicated in the graph of the following function:
(1.25 * y-sqrt (abs (x))) ^ 2 + x ^ 2-1,

I have used the Taks: the Second Derivative Test. Without results, as I show below:

Heart_Critical_Points_and_the_Second_Derivative_Test.mw
 

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Critical Points and the Second Derivative Test

Objective Function f
> 

(1.25*y-sqrt(abs(x)))^2+x^2-1

(1.25*y-abs(x)^(1/2))^2+x^2-1

 (1)
> 

smartplot[x, y]((1.25*y-sqrt(abs(x)))^2+x^2-1 = 0)

 
> 

 

> 

 

List of Independent Variables
> 

v := [x, y]

[x, y]

 (2)

Equations Nabla(f) = 0
> 

convert(Student[MultivariateCalculus][Gradient]((1.25*y-abs(x)^(1/2))^2+x^2-1, [x, y]), list)

[-(1.25*y-abs(x)^(1/2))*abs(1, x)/abs(x)^(1/2)+2*x, 3.1250*y-2.50*abs(x)^(1/2)]

 (3)

Critical Points
> 

temp := remove(has, solve([-(1.25*y-abs(x)^(1/2))*abs(1, x)/abs(x)^(1/2)+2*x, 3.1250*y-2.50*abs(x)^(1/2)], v, Explicit), I); convert({seq(eval(v, temp[k]), k = 1 .. nops(temp))}, list)

[]

 (4)

Second Derivative Test
> 

Student[MultivariateCalculus][SecondDerivativeTest]((1.25*y-abs(x)^(1/2))^2+x^2-1, v = [])

LocalMin = [], LocalMax = [], Saddle = []

 (5)

Hessians and their Eigenvalues
> 

Temp := [Student[MultivariateCalculus][SecondDerivativeTest]((1.25*y-abs(x)^(1/2))^2+x^2-1, v = [], output = hessian)]; for k to nops(Temp) do Temp[k], convert(LinearAlgebra[Eigenvalues](Temp[k]), list) end do

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

  
 

 

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Download Heart_Critical_Points_and_the_Second_Derivative_Test.mw

 

 

 
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