# Intervals of increase/ decrease

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Over which interval is f(x) = x^3 - 12x^2 + 36x + 1 decreasing?

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#### Solution Preview

See the attached file.

We set y' = 3x^2 - 24x + 36 = 0 and solve for x

3x^2 - 24x + 36 = 0

implies that x^2 - 8x + 12 = ...

#### Solution Summary

A function can be increasing or decreasing in an interval. To ascertain the intervals of increase or decrease the derivative test is used as illustrated in this problem.

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