Math Problem Statement

Identify the coordinates of any local and absolute extreme points and inflection points. Graph the function. yequalsStartFraction 9 x Over x squared plus 9 EndFraction Question content area bottom Part 1 Identify the coordinates of the local maximum points. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The local maximum​ point(s) is/are    left parenthesis 3 comma three halves right parenthesis . ​(Type an ordered pair. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.) Your answer is correct.B. There are no local maximum points. Part 2 Identify the coordinates of the local minimum points. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The local minimum​ point(s) is/are    left parenthesis negative 3 comma negative three halves right parenthesis . ​(Type an ordered pair. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.) Your answer is correct.B. There are no local minimum points. Part 3 Identify the coordinates of the absolute maximum points. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The absolute maximum​ point(s) is/are    left parenthesis 3 comma three halves right parenthesis . ​(Type an ordered pair. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.) Your answer is correct.B. There are no absolute maximum points. Part 4 Identify the coordinates of the absolute minimum points. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The absolute minimum​ point(s) is/are    left parenthesis negative 3 comma negative three halves right parenthesis . ​(Type an ordered pair. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.) Your answer is correct.B. There are no absolute minimum points. Part 5 Find the inflection points. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The inflection​ point(s) is/are    enter your response here. ​(Type an ordered pair. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as​ needed.) B. There are no inflection points.

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Derivatives
Extrema
Inflection Points

Formulas

First derivative: f'(x) = [(x^2 + 9)(9) - 9x(2x)] / (x^2 + 9)^2
Second derivative: Use quotient rule to differentiate the first derivative

Theorems

First Derivative Test
Second Derivative Test
Quotient Rule

Suitable Grade Level

Grades 11-12 or Calculus I