Math Problem Statement

Use the graph to identify the points on the interval left bracket a comma b right bracket at which local and absolute extreme values occur. Question content area bottom left Part 1 List the​ x-values where local minima​ occur, if any. Select the correct choice​ and, if​ necessary, fill in the answer box to complete your choice. A. The local minimum​ value(s) occur(s) at xequals    q comma s. ​(Use a comma to separate answers as​ needed.) Your answer is correct.B. There is no local minimum. Part 2 List the​ x-values where local maxima​ occur, if any. Select the correct choice​ and, if​ necessary, fill in the answer box to complete your choice. A. The local maximum​ value(s) occur(s) at xequals    r. ​(Use a comma to separate answers as​ needed.) Your answer is correct.B. There is no local maximum. Part 3 List the​ x-values where absolute minima​ occur, if any. Select the correct choice​ and, if​ necessary, fill in the answer box to complete your choice. A. The absolute minimum​ value(s) occur(s) at xequals    enter your response here. ​(Use a comma to separate answers as​ needed.) B. There is no absolute minimum. . . . Question content area right Part 1 a q r s b x y y equals f left parenthesis x right parenthesis

A coordinate system has an unlabeled vertical y-axis and a horizontal x-axis with the following labeled values, listed from left to right: a, q, r, s, and b. A curve labeled y equals f left parenthesis x right parenthesis starts above the x-axis at a and falls from left to right until reaching q. Then the curve rises from left to right until reaching r, which is below the previous location of the curve at a. Next, the curve falls from left to right until reaching s. At s, the curve is below the previous location of the curve at q. The curve has a cusp at s. Finally, the curve rises from left to right until ending at b. At b, the curve is still below the previous location of the curve at q. There are vertical dashed lines extending from the labeled values on the x-axis to the curve.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Graph Analysis
Extrema
Intervals

Formulas

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Theorems

Extreme Value Theorem
Local Extrema Identification

Suitable Grade Level

Grades 11-12