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If the derivative of a function equals xsquared - 2divided byx on which intervals is f decreasing?
Wiki User
∙ 14y ago
f(x) is decreasing on the interval on which f'(x) is negative.
So we want:
(x2-2)/x<0
For this to be true either the numerator or the denominator (but not both) must be negative.
On the interval x>0, the numerator is negative for 0<x<sqrt(2) and the denominator is positive for all x>0.
On the interval x<0, the denominator is negative for all values on this interval. The numerator is positive on this interval for x<-sqrt(2).
So, f' is negative (and f is decreasing) on the intervals: (-infinity, -sqrt(2)), (0, sqrt(2))
Wiki User
∙ 14y ago
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