Math Problem Statement
For the function f(x), find the maximum number of real zeros, the maximum number of x-intercepts, and the maximum number of turning points that the function can have.
f(x)equals=x Superscript 6 Baseline minus x squared plus 9
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Polynomials
Zeros of Functions
Turning Points
X-Intercepts
Formulas
The maximum number of real zeros of a polynomial corresponds to its degree
The maximum number of turning points is given by n - 1, where n is the degree of the polynomial
Theorems
Fundamental Theorem of Algebra: A polynomial of degree n has exactly n roots (real or complex)
Turning Point Theorem: A polynomial of degree n can have at most n - 1 turning points
Suitable Grade Level
Grades 10-12
Related Recommendation
Finding Real Zeros, x-Intercepts, and Turning Points of f(x) = x^7 - x^2 + 8
Analyze Polynomial Function f(x) = (x - 7)^3 (x + 9)^2 - Zeros, Multiplicity, and Graph Behavior
Determine Maximum Turning Points for Polynomial Function f(x) = 2x^3 + 3x^2 + 3
Analyzing a Polynomial Function: Turning Points, Zeros, and Division
Analyzing Polynomial Function: Real Zeros, Multiplicity, and End Behavior of f(x) = (x - 3)^3(x + 1)^2