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
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