Math Problem Statement

For each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum. (Enter your answers as comma-separated lists.)

The x y-coordinate plane is given. A curve with three parts is graphed. The x−axis has values labeled a, b, c, d, r, and s. The curve begins at a closed point above x = a at its lowest point on the graph, goes up and right becoming less steep, ends at a closed point above x = b, begins again at an open point directly below the previous point and above x = b, goes up and right becoming less steep, ends at an open point above x = c, begins again at a closed point below the previous point and above x = c, goes down and right becoming less steep, changes direction at a point above x = d, goes up and right becoming more steep, sharply changes direction at its highest point on the graph above x = r, goes down and right becoming less steep, and ends at a closed point above x = s. absolute maximum

absolute minimum

local maximum

local minimum

neither a maximum nor a minimum

Solution

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Math Problem Analysis

Mathematical Concepts

Graph Analysis
Functions
Local and Absolute Extrema

Formulas

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Theorems

First Derivative Test
Maximum and Minimum Theorems

Suitable Grade Level

Grades 11-12