The given function presents a local minimum in the coordinates (0,-1).
Factoring
In math, factoring or factorization is used to write an algebraic expression in factors. There are some rules for factorization. One of them is a factor out a common term for example: x²-x= x(x-1), where x is a common term.
For solving this question, the given equation should be rewritten from the factoring.
[tex]x^5-x^3+x^2-1=\left(x+1\right)^2\left(x-1\right)\left(x^2-x+1\right)=0[/tex]. Then, you have 3 equations.
From the Zero Factor Principle, you can write
Equation 1
(x+1)²=0
x+1=0
x= -1
Equation 2
x-1=0
x=1
Equation 3
x²-x+1=0
[tex]x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\cdot \:1\cdot \:1}}{2\cdot \:1}\\ \\ x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{3}i}{2\cdot \:1}[/tex]
From these points it is possible to plot a graph and you can see that the local minimum presents the coordinates (0,-1).
Read more about the factoring here:
brainly.com/question/11579257
#SPJ1
