Math Problem Statement
Consider a function f(x)=a x^{3}+b x^{2}+c x+d, with three real roots x_{0}, x_{1}, x_{2} such that x_{0}<x_{1}<x_{2}. Show that there must be a local maximum between x_{0} and x_{1} and a local minimum between x_{1} and x_{2}.
Solution
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Math Problem Analysis
Mathematical Concepts
Polynomials
Cubic Functions
Derivatives
Local Extrema
Formulas
Quadratic formula
Theorems
Intermediate Value Theorem
Suitable Grade Level
Grades 11-12
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