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

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:



Critical Points and the Second Derivative Test

Objective Function f




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




List of Independent Variables

v := [x, y]

[x, y]


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)]


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)



Second Derivative Test

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

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


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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