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Focus B: Instantaneous Rate of Change

Test yourself (Solution)

Height of water at 0.5 sec:

Height of water at 0.501 sec.

Average rate of change in height compared to time is the slope of the secant line through these two points:

Since the points are "very close" together, we can use this as an approximation to the slope of the tangent at the point t = 0.5 which is the instantaneous rate of change at that point.

Thus the rate of change in height at 0.5 sec is approximately 1.4 cm/sec.