Revisiting Average Rates of Change, Using Integrals
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Problems 15
- Given the function g(t)g(t)g(t) graphed above, find the average rate of change on the interval [0,3][0,3][0,3].
- On a road trip, after picking up your friend who lives 10 miles away, you decide to record your distance from home over time. Find your average speed over the first 6 hours.
- Compute the average rate of change of f(x)=x2−1x f(x)=x^2-\dfrac{1}{x}\;f(x)=x2−x1 on the interval [2, 4].
- Find the average rate of change of g(t)=t2+3t+1g(t)=t^2+3t+1g(t)=t2+3t+1 on the interval [0,a][0,a][0,a]. Your answer will be an expression involving aaa.
- Find the average rate of change of f(x)=x3+2f(x)=x^3+2f(x)=x3+2 on the interval [a,a+h][a,a+h][a,a+h]. Your answer will be an expression involving aaa.
- Find the average rate of change of f(x)=x−2x f(x)=x-2\sqrt x\;f(x)=x−2x on the interval [1,9][1,9][1,9].
- Based on the graph above, estimate the average rate of change from x=1x=1x=1 to x=4x=4x=4.
- Based on the graph above, estimate the average rate of change from x=2x=2x=2 to x=5x=5x=5, to the nearest hundredth.
- Find the average rate of change f(x)=x2f(x)=x^2f(x)=x2 on [1,5][1,5][1,5].
- Find the average rate of change q(x)=x3q(x)=x^3q(x)=x3 on [−4,2][-4,2][−4,2].
- Find the average rate of change g(x)=3x3−1g(x)=3x^3-1g(x)=3x3−1 on [−3,3][-3,3][−3,3]
- Find the average rate of change h(x)=5−2x2h(x)=5-2x^2h(x)=5−2x2 on [−2,4][-2,4][−2,4]
- Find the average rate of change k(t)=6t2+4t3k(t)=6t^2+\dfrac{4}{t^3}k(t)=6t2+t34 on [−1,3][-1,3][−1,3]. Round to the nearest whole number.
- Find the average rate of change k(t)=t2−4t+1t2+3k(t)=\dfrac{t^2-4t+1}{t^2+3}k(t)=t2+3t2−4t+1 on [−3,1][-3,1][−3,1]
- Find the average rate of change of a(t)=1t+4a(t)=\dfrac{1}{t+4}a(t)=t+41 on [9,9+h][9,9+h][9,9+h]. Your answer will be expressed involving hhh.