Find the intervals on which the function is increasing and the intervals on which the function is decreasing.
-f(x)= -x2 + 10x + 24
A)Increasing on (- 5, ); decreasing on (- , - 5)
B)Increasing on (- , 5); decreasing on (5, )
C)Increasing on (- , - 5); decreasing on (- 5, )
D)Increasing on (5, ); decreasing on (- , 5)

Question

Quizplus · Accepted Answer

To determine where the function is increasing or decreasing, we first find its derivative: f'(x) = -2x + 10. Setting f'(x) = 0 gives x = 5. This is the critical point where the function changes from increasing to decreasing or vice versa. For x < 5, f'(x) > 0, meaning the function is increasing. For x > 5, f'(x) < 0, meaning the function is decreasing. Therefore, the function is increasing on (-∞, 5) and decreasing on (5, ∞).

Find the Intervals on Which the Function Is Increasing and the Intervals