Respuesta :
The extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
What is extreme value of a polynomial?
Extreme values of a polynomial are the peaks and valleys of the polynomial—the points where direction changes.
What are the steps of finding the extreme value of any polynomial?
The following steps which are required to find the extreme value of polynomial are:
- Arrange the polynomial into the the form of [tex]ax^{2} +bs+c[/tex] where a, b and c are numbers.
- Determine whether a, the coefficient of the [tex]x^{2}[/tex] term, is positive or negative.
- If the term is positive, the extreme value will be the infinity because the value will continue to grow as x increases.
- If it is negative, use the formula [tex]\frac{-b}{2a}[/tex] to find the value for extreme.
- And then plug [tex]x = \frac{-b}{2a}[/tex] in the original polynomial to calculate the extreme value of the polynomial.
According to the given question.
We have a polynomial
[tex]f(x) = x^{2} -4[/tex]
Since, in the given polynomial the coefficient of [tex]x^{2}[/tex] is positive . Therefore, the extreme value of the given polynomial is infinity because the value will continue to grow as x increases.
Hence, the extreme value of the given polynomial [tex]f(x) = x^{2} -4[/tex] is ∞.
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