A weight that is attached to the end of a spring is pulled and then released. The function H gives its height, in centimeters, after t seconds. What is the best interpretation for the following statement? H^(')(0)=3 Choose 1 answer: (A) When the weight is released, its height is 3 centimeters. (B) When the weight is released, its mass is increasing at a rate of 3 grams per second. (C) When the weight is released, its height is increasing at a rate of 3 . (D) When the weight is released, its height is increasing at a rate of 3 centimeters per second.

Question

A weight that is attached to the end of a spring is pulled and then released. The function  H gives its height, in centimeters, after  t seconds. What is the best interpretation for the following statement?  H^(')(0)=3 Choose 1 answer: (A) When the weight is released, its height is 3 centimeters. (B) When the weight is released, its mass is increasing at a rate of 3 grams per second. (C) When the weight is released, its height is increasing at a rate of 3 . (D) When the weight is released, its height is increasing at a rate of 3 centimeters per second.

Bytelearn · Accepted Answer

Definition of Derivative: H^(')(0)=3 means the derivative of the height function H with respect to time t is 3 when t equals 0.Rate of Change Interpretation: The derivative represents the rate of change of the height with respect to time.Initial Rate of Change: Since the derivative is taken at t=0, it describes the initial rate of change of the height right after the weight is released.Rate of Change at t=0: The value of the derivative is 3, which means the height is increasing at a rate of 3 centimeters per second at t=0.

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