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Determining the Critical Numbers of a Piecewise Function?
f’(x)= - 2x for x≤0
f’(x)= - 2 for x>0
How do I go about finding the critical number(s) to determine relative max/min and the open intervals upon which the function is increasing or decreasing?
1 Answer
- SqdancefanLv 75 years agoFavorite Answer
The only piece of your piecewise function that will have f'(x) = 0 is the piece defined for x ≤ 0. f'(x) = 0 at x = 0.
The function is increasing (f' > 0) elsewhere in that interval (x < 0), and is decreasing in the interval x > 0, where f' is negative.
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To figure this out, you need to think about what the definition of f'(x) is telling you.
