Average and Instantaneous Rates of Change

Question

For the functions $$x(t)=t^3-2*t$$ and $$y(t)=4*t-t^2$$, all of the following statements about their rates of change on the interval [1, 3] are true EXCEPT:

Accepted Answer

The average rate of change of $$y(t)$$ over the interval [1, 3] is 1.

Answer

The instantaneous rate of change of $$x(t)$$ is given by differentiating to obtain $$3*t^2-2$$.

Answer

The average rate of change of a function over an interval generally does not equal its instantaneous rate at the midpoint of the interval.

Answer

Differentiating $$y(t)$$ yields an instantaneous rate of change of $$4-2*t$$.

Average and Instantaneous Rates of Change

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