Math Problem Statement
Determine the behavior of the function f(x) = x^2 - ax^2 - bx + 12 in terms of increasing/decreasing intervals, concavity, and critical points.
Solution
Let's analyze the questions in your image step-by-step:
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Determine the direction of :
- This appears to be asking for an analysis of the function's behavior, specifically its increasing and decreasing intervals. You would typically take the derivative of , set to find critical points, and analyze these points to determine whether is increasing or decreasing around them.
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Concave up or down:
- This part is about the concavity of the function, which involves the second derivative .
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Math Problem Analysis
Mathematical Concepts
Calculus
Function Analysis
Derivative
Second Derivative
Concavity
Critical Points
Formulas
f'(x) = derivative of f(x)
f''(x) = second derivative of f(x)
Theorems
First Derivative Test
Second Derivative Test
Suitable Grade Level
Grades 10-12
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