Math Problem Statement
For the polynomial function g, the rate of change of g is increasing for x<2 and decreasing for x>2. which of the following must be true?
1, the graph of g has a minimum at x=2 2. the graph of g has a maximum of x=2 3. the graph of g has a point of inflection at x=2, is concave down for x<2, and is concave up for x>2 4. the graph of g has a point of inflection at x=2, is concave up for x<2, and is concave down for x>2
Solution
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Math Problem Analysis
Mathematical Concepts
Calculus
Derivatives
Concavity
Points of Inflection
Formulas
First derivative: g'(x)
Second derivative: g''(x)
Theorems
Inflection point: A point where the concavity of the function changes.
Concavity: g''(x) > 0 for concave up, g''(x) < 0 for concave down.
Suitable Grade Level
Grades 11-12 (Pre-Calculus or Calculus)