The degree of [tex]f(x)[/tex] is 4 and the leading coefficient is a negative number. There are two distinct real zeros and two relative minimum values.
Procedure - Determination of characteristics of a polynomic function
Based on the form of the figure, we observe the following characteristics:
- The maximum grade of the polynomial must be even since [tex]y < 0[/tex] for both [tex]x \to -\infty[/tex] and [tex]x \to + \infty[/tex]. The leading coefficient must be negative.
- The least grade of the polynomial must be 4.
- The function has two real zeros.
- The function has two relative maxima.
Therefore, we have the following conclusion: The degree of [tex]f(x)[/tex] is 4 and the leading coefficient is a negative number. There are two distinct real zeros and two relative minimum values.
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