Answer:
The given function is:
f(x) = -3x^2 + 12
To find the interval over which the function is increasing, we need to find the critical points of the function.
f'(x) = -6x
The critical point is where f'(x) = 0
-6x = 0
x = 0
Now, we need to check the sign of f'(x) on either side of the critical point to determine whether the function is increasing or decreasing.
If x < 0, then f'(x) < 0, so the function is decreasing.
If x > 0, then f'(x) > 0, so the function is increasing.
Therefore, the interval over which the function is increasing is:
(0, infinity)
Explanation:
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