For the function below, find a) the critical numbers; b) the open intervals wher

Question

For the function below, find a) the critical numbers; b) the open intervals where the function is increasing; and c) the open intervals where it is decreasing. f(x) = 8x3 - 6x2 - 72x + 1 Find the critical number(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The critical number(s) is/are . (Use a comma to separate answers as needed.) There are no critical numbers. List any interval(s) on which the function is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The function is increasing on the interval(s) . (Type your answer in interval notation. Use a comma to separate answers as needed.) The function is never increasing. List any interval(s) on which the function is decreasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. The function is decreasing on the interval(s) . (Type your answer in interval notation. Use a comma to separate answers as needed. The function is never decreasing.

Explanation / Answer

a)f'(x)=0 ==>24x^2 -12x -72=0 ==>2x^2-x-6=0 ==>2x^2-4x+3x-6=0 ==>x=2,-3/2 b)function is increasing (-infinity,-3/2)U(2,infinity) c)function is decreasing (-3/2 ,2)

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