Math Problem Statement
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Critical Points
Derivatives
Concavity
Inflection Points
Formulas
f'(x) = (3/5)x^(-2/5)(x - 7) + x^(3/5)
f'(x) = x^(-2/5)(8x - 21)/5
Critical points where f'(x) = 0
Concavity determined by f''(x)
Theorems
First Derivative Test for increasing/decreasing intervals
Second Derivative Test for concavity and inflection points
Suitable Grade Level
Undergraduate - Calculus I
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