APFIVE Interpretation of the Derivative at a Point
Which of the following statements best interprets the derivative of a function f at a point a?
A
It represents the average rate of change of the function over an interval that includes a, summarizing overall behavior rather than the instantaneous rate.
B
It indicates that the function is necessarily increasing at a because the derivative is associated only with upward trends.
C
It is the slope of the tangent line to the graph of f at a, representing the instantaneous rate of change at that point.
D
It gives the maximum value that the function f can achieve near the point a, indicating a local peak.
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