Math Problem Statement

The function f(x)=8x+2x^-1 has one local minimum and one local maximum. This function has a local maximum at x= with value

and a local minimum at x= with value

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Differentiation
Critical Points
Second Derivative Test

Formulas

f(x) = 8x + 2x^-1
f'(x) = 8 - 2x^-2
f''(x) = 4/x^3

Theorems

Second Derivative Test

Suitable Grade Level

Grades 11-12