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\left(x\right)=x^{7}-x^{2}+8

Solution

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Math Problem Analysis

Mathematical Concepts

Polynomial Functions
Zeros of Polynomials
Turning Points
Intercepts

Formulas

The maximum number of real zeros of a polynomial is equal to its degree
The maximum number of turning points of a polynomial function is n - 1, where n is the degree of the polynomial

Theorems

Fundamental Theorem of Algebra

Suitable Grade Level

Grades 10-12