(a) Over what interval(s) (a) through (d) is the rate of change of f (x) positive?
(b) Over what interval(s) (a) through (d) is the rate of change of f (x) negative?
Because the derivative of a function represents both the slope of the tangent to the curve and the instantaneous rate of change of the function, it is possible to use information about one to gain information about the other.

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E B a P b