Math Problem Statement

Use analytical methods to find all local extrema of the function ​f(x)equals=5x Superscript x​, for xgreater than>0. Verify your work using a graphing utility.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Extrema
Exponential Functions

Formulas

f(x) = 5x^x
Derivative of x^x: d/dx(x^x) = e^(x ln(x)) (ln(x) + 1)

Theorems

First Derivative Test
Second Derivative Test

Suitable Grade Level

University Calculus Level