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For the function 8-(x-3)^2

find the interval(s) over which the function is increasing

User Ttugates
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1 Answer

5 votes

To find the interval(s) over which the function 8-(x-3)^2 is increasing, we need to find the critical points of the function and test the sign of the derivative on either side of these points.

The derivative of the function 8-(x-3)^2 is -2(x-3).

Setting the derivative equal to zero to find the critical points:

-2(x-3) = 0

x = 3

Testing the sign of the derivative on either side of x = 3:

-2(x-3) is negative for x < 3, meaning the function is decreasing on the interval (-infinity, 3).

-2(x-3) is positive for x > 3, meaning the function is increasing on the interval (3, infinity).

Therefore, the interval over which the function 8-(x-3)^2 is increasing is (3, infinity).

User Antonio Favata
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