Question

Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing, as well as where it is concave up or concave down: f(x) = 3x^2 + 36x What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The coordinates of the relative extrema are (Simplify your answer. Type an ordered pair. Type an exact answer using radicals as needed. Use integers or fractions for any numbers in the expression. Use comma to separate answers as needed.) B. There are no relative extrema. What are the coordinates of the inflection points? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The coordinates of the inflection points are (Simplify your answer. Type an ordered pair. Type an exact answer using radicals as needed. Use integers or fractions for any numbers in the expression. Use comma to separate answers as needed.) B. There are no inflection points. On what interval(s) is the function increasing or decreasing? A. The function is increasing on (-∞, 0) and (2, ∞). The function is decreasing on (0, 2). B. The function is never increasing. The function is decreasing on (-∞, 0). C. The function is increasing on (-∞, ∞). The function is never decreasing. D. The function is increasing on (0, ∞). The function is decreasing on (-6, 0).

          Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing, as well as where it is concave up or concave down:

f(x) = 3x^2 + 36x

What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The coordinates of the relative extrema are (Simplify your answer. Type an ordered pair. Type an exact answer using radicals as needed. Use integers or fractions for any numbers in the expression. Use comma to separate answers as needed.) 
B. There are no relative extrema.

What are the coordinates of the inflection points? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The coordinates of the inflection points are (Simplify your answer. Type an ordered pair. Type an exact answer using radicals as needed. Use integers or fractions for any numbers in the expression. Use comma to separate answers as needed.) 
B. There are no inflection points.

On what interval(s) is the function increasing or decreasing?

A. The function is increasing on (-∞, 0) and (2, ∞). The function is decreasing on (0, 2). 
B. The function is never increasing. The function is decreasing on (-∞, 0).
C. The function is increasing on (-∞, ∞). The function is never decreasing.
D. The function is increasing on (0, ∞). The function is decreasing on (-6, 0).

Added by Alicia C.

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