Math Problem Statement

f(x) = x^3+4x^2-5x+2

Solution

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Math Problem Analysis

Mathematical Concepts

Algebra
Calculus
Polynomial Functions
Derivative Analysis
Concavity

Formulas

f(x) = x^3 + 4x^2 - 5x + 2
First derivative: f'(x) = 3x^2 + 8x - 5
Second derivative: f''(x) = 6x + 8

Theorems

Intermediate Value Theorem for finding roots
First Derivative Test for identifying increasing and decreasing intervals
Second Derivative Test for concavity and inflection points

Suitable Grade Level

Grades 11-12