Math Problem Statement
Solve the problem.
The total cost of producing x units of a certain commodity is C(x) thousand dollars, where
C(x) = x3 - 14x2 + 163x + 128
The average cost function is A(x) = . For what values of x is A(x) increasing? For what values is it decreasing? Group of answer choices
Increasing; x > 16; decreasing: 0 < x < 16
Increasing; 0 < x < 16; decreasing: x > 16
Increasing; x > 8; decreasing: 0 < x < 8
Increasing; 0 < x < 8; decreasing: x > 8
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Cost Functions
Critical Points
Formulas
Average cost function: A(x) = C(x)/x
Derivative of A(x): A'(x) = 2x - 14 - 128/x^2
Critical point: x = 8
Theorems
Derivative Test for Increasing/Decreasing Functions
Suitable Grade Level
Grades 11-12
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