Math Problem Statement
Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.)
f(x) = 8x −
2
x
on [2, 4]
maximum minimum
Solution
To find the absolute maximum and minimum values of the function on the interval , we need to follow these steps:
- Compute the derivative of and set it equal to zero to find critical points.
- Evaluate the function at the endpoints of the interval and at any critical points within the interval.
- Compare these values to determine the absolute maximum and minimum.
Step 1: Find
The function is: Differentiating with respect to :
To find critical points, set : However, solving
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Math Problem Analysis
Mathematical Concepts
Calculus
Optimization
Critical Points
Formulas
f(x) = 8x - 2/x
f'(x) for finding critical points
Evaluating f(x) at endpoints
Theorems
Extreme Value Theorem
Derivative for finding critical points
Suitable Grade Level
College Calculus
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