The distance covered by a train after $t$ hours is $D(t)=3t^2+7t$ kilometers, and $D^{\prime }(t)=6t+7$. What is the instantaneous rate of change at $t=6$?

The temperature of an oven is $T(t)$, in degrees Celsius, at time $t$ in minutes: $T(0)=8$, $T(6)=38$, $T(8)=64$, $T(10)=74$. What is the average rate of change from $t=6$ to $t=8$?

Find the average rate of change of $v(x)=-4x^2-7x+2$ on the interval $\left[-5,1\right]$.

The height of a seedling after $t$ days is $H(t)=5t^2+8t$ centimeters, and $H^{\prime }(t)=10t+8$. What is the instantaneous rate of change at $t=3$?

The balance of an account after $t$ weeks is $B(t)=3t^2+t$ dollars, and $B^{\prime }(t)=6t+1$. What is the instantaneous rate of change at $t=3$?

The temperature of an oven is $T(t)$, in degrees Celsius, at time $t$ in minutes: $T(0)=2$, $T(1)=7$, $T(5)=31$, $T(7)=41$. What is the average rate of change from $t=1$ to $t=5$?

Find the average rate of change of $g(x)=4x^2+2x+6$ on the interval $\left[2,6\right]$.

A car's odometer reads $20$ miles at 3 o'clock and $245$ miles 5 hours later, and its speedometer reads $41$ miles per hour at the end of the trip. Which statement correctly names these two quantities?

The figure shows the graph of $w$, with a secant segment drawn through the two marked points. What is the average rate of change of $w$ on $\left[0,2\right]$?

The distance covered by a train is $D(t)$, in kilometers, at time $t$ in hours: $D(0)=6$, $D(1)=10$, $D(7)=46$, $D(9)=54$. What is the average rate of change from $t=1$ to $t=7$?

Find the average rate of change of $w(x)=2x^2+7x-3$ on the interval $\left[-3,1\right]$.

A car's odometer reads $70$ miles at 5 o'clock and $305$ miles 5 hours later, and its speedometer reads $43$ miles per hour at the end of the trip. Which statement correctly names these two quantities?

Find the average rate of change of $w(x)=x^2-8x-4$ on the interval $\left[-5,-3\right]$.

The figure shows the graph of $g$, with a secant segment drawn through the two marked points. What is the average rate of change of $g$ on $\left[-1,1\right]$?

A car's odometer reads $20$ miles at 2 o'clock and $200$ miles 4 hours later, and its speedometer reads $40$ miles per hour at the end of the trip. Which statement correctly names these two quantities?

The mass of a melting block after $t$ hours is $M(t)=4t^2+5t$ grams, and $M^{\prime }(t)=8t+5$. What is the instantaneous rate of change at $t=4$?

A car's odometer reads $30$ miles at 2 o'clock and $302$ miles 4 hours later, and its speedometer reads $63$ miles per hour at the end of the trip. Which statement correctly names these two quantities?

The figure shows the graph of $q$, with a secant segment drawn through the two marked points. What is the average rate of change of $q$ on $\left[-1,3\right]$?

A car's odometer reads $40$ miles at 7 o'clock and $168$ miles 2 hours later, and its speedometer reads $54$ miles per hour at the end of the trip. Which statement correctly names these two quantities?

A car's odometer reads $40$ miles at 5 o'clock and $228$ miles 4 hours later, and its speedometer reads $42$ miles per hour at the end of the trip. Which statement correctly names these two quantities?

The mass of a melting block is $M(t)$, in grams, at time $t$ in hours: $M(0)=4$, $M(4)=24$, $M(8)=52$, $M(10)=62$. What is the average rate of change from $t=4$ to $t=8$?

The temperature of an oven after $t$ minutes is $T(t)=t^2+9t$ degrees Celsius, and $T^{\prime }(t)=2t+9$. What is the instantaneous rate of change at $t=5$?

Find the average rate of change of $p(x)=-x^2-7x$ on the interval $\left[5,11\right]$.

The volume of water in a tank is $V(t)$, in liters, at time $t$ in minutes: $V(0)=3$, $V(1)=7$, $V(4)=25$, $V(6)=33$. What is the average rate of change from $t=1$ to $t=4$?

The figure shows the graph of $r$, with a secant segment drawn through the two marked points. What is the average rate of change of $r$ on $\left[-1,1\right]$?

The distance covered by a train after $t$ hours is $D(t)=2t^2+6t$ kilometers, and $D^{\prime }(t)=4t+6$. What is the instantaneous rate of change at $t=6$?

Find the average rate of change of $p(x)=-4x^2-6x+2$ on the interval $\left[-1,5\right]$.

The volume of water in a tank is $V(t)$, in liters, at time $t$ in minutes: $V(0)=4$, $V(5)=34$, $V(13)=90$, $V(15)=102$. What is the average rate of change from $t=5$ to $t=13$?

Find the average rate of change of $v(x)=-2x^2-2x$ on the interval $\left[5,7\right]$.

Find the average rate of change of $v(x)=3x^2-2x-6$ on the interval $\left[1,4\right]$.