Math Problem Statement

If this is the derivative graph what does the function look like?

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivative Analysis
Critical Points
Intervals of Increase and Decrease
Concavity and Inflection Points

Formulas

f'(x) = 0 at critical points
Sign of f'(x) indicates increasing/decreasing behavior of f(x)

Theorems

First Derivative Test
Concavity Test

Suitable Grade Level

Grades 11-12