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Derivatives: Rate of Change

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Wize University Calculus 1 Textbook > Derivatives

Derivatives as a Rate of Change

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In recent years, exports from Canada to the United States are on the rise. Let E(t)E(t) represent the amount of exports to the United States from Canada (in Billions of dollars) at time tt. Let tt be the number of years after 2000. Interpret the following statements without using the words "derivative" or "instantaneous rate of change".

E(2)=5E(2)=5

E′(3)=1E'(3)=1

E′(15)>E′(0)E'(15)>E'(0)


More Derivatives as a Rate of Change Questions:
Derivatives and Tangent Lines
A certain particle is traveling through space and time. We are able to measure the position of the particle at certain time values. Although we can't measure the particle continuously, we know that the particles position function is differentiable. The table gives values of time for the differentiable function s(t) for 0≤t≤40\le t\le4. s(t) represents the position of the particle at time t.
Practice: Derivatives as a Rate of Change
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Practice: Average Rate of Change & the Secant Line
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Average Rate of Change & the Secant Line
Practice: Average Rate of Change & the Secant Line
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Average Rate of Change & the Secant Line
Practice: Average Rate of Change & the Secant Line
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t01234P10001305152817741936\begin{array}{|r|c|c|c|c|c|}\hline \textbf{t}&0&1&2&3&4\\\hline \textbf{P}&1000&1305&1528&1774&1936\\\hline \end{array}
Average Rate of Change & the Secant Line
Practice: Average Rate of Change & the Secant Line
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t01234A150183204247283\begin{array}{|r|c|c|c|c|c|}\hline \textbf{t}&0&1&2&3&4\\\hline \textbf{A}&150&183&204&247&283\\\hline \end{array}
Average Rate of Change & the Secant Line
Practice: Average Rate of Change & the Secant Line
Determine the average rate of the change of the function g(t)=−3t2t+5g(t)=\dfrac{-3t}{2t+5} over the interval 0≤t≤50\leq{}t\leq{}5.
Average Rate of Change & the Secant Line
Practice: Average Rate of Change & the Secant Line
Determine the average rate of the change of the function g(t)=t2t2−6g(t)=\dfrac{t^2}{t^2-6} over the interval 0.5≤t≤20.5\leq{}t\leq{}2.
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f′(x)f'(x) plot for a differentiable function is depicted as below. Find interval(s) for which f(x)f\left(x\right) is increasing.
The average rate of change of the function f(x)=2cos⁡(x)f(x)=2\cos(x) over the interval [π6,π2][ \frac{\pi}{6},\frac{\pi}{2}] is
Derivatives and Tangent Lines
A certain particle is traveling through space and time. We are able to measure the position of the particle at certain time values. Although we can't measure the particle continuously, we know that the particles position function is differentiable. The table gives values of time for the differentiable function s(t) for 0≤t≤40\le t\le4. s(t) represents the position of the particle at time t.
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