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) = x^3 - 27x
What are the coordinates of the relative extrema? Select the correct choice below and 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 a 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 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 a 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 f is increasing on (0, β). The function f is decreasing on (-β, 0).
B. The function f is increasing on (-β, 0). The function f is decreasing on (0, β).
C. The function f is increasing on (3, β). The function f is decreasing on (-β, 3).
D. The function f is increasing on (-β, -3) and (3, β). The function f is decreasing on (-3, 3).
E. The function f is decreasing on (-β, -3) and (3, β). The function f is increasing on (-3, 3).
On what interval(s) is the function concave up or concave down?
A. The function is concave up on (0, β). The function is concave down on (-β, 0).
B. The function is concave up on (-β, 0). The function is concave down on (0, β).
C. The function is concave up on (-β, 3) and (3, β). The function is concave down on (-3, 3).
D. The function is concave up on (0, 0). The function is concave down on (0, β).
E. The function is never concave up. The function is concave down on (-6, 0) and (0, 0).
F. The function is concave up on (-3, 3). The function is concave down on (-β, -3) and (3, β).
G. The function is concave up on (-β, 0) and (0, β). The function is never concave down.