Math Problem Statement
Find the open intervals on which the function f(x)=x+10√1-x is increasing or decreasing. The safe points will be calculated from these intervals. If the function is never increasing or decreasing, provide an input of NA to your computer.
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Increasing and Decreasing Functions
Formulas
f'(x) = 1 - (5/√(1 - x))
Domain constraint: 1 - x ≥ 0
Theorems
Chain Rule
Critical Points Analysis
Suitable Grade Level
Grades 11-12 (or early college level)
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