For $f(x)=x^2$ on $\left[0,5\right]$, the Mean Value Theorem for Integrals guarantees a $c$ in $\left(0,5\right)$ with $f(c)$ equal to the average value. What is $c$?

The Mean Value Theorem for Integrals is applied to $f(x)=x^2+1$ on $\left[2,5\right]$. Which hypothesis does the theorem require?

Water flows into a tank at a rate $r(t)=t^2$ gallons per minute for $0\le t\le 3$ minutes. What is the average flow rate over that interval?

What is the average value of $f(x)=x^3$ on $\left[3,7\right]$?

What is the average value of $f(x)=2e^{-x}$ on $\left[0,4\right]$?

What is the average value of $f(x)=7e^{-x}$ on $\left[0,1\right]$?

What is the average value of $f(x)=4e^{-x}$ on $\left[0,4\right]$?

What is the average value of $f(x)=x^2$ on $\left[4,5\right]$?

What is the average value of $f(x)=x^3$ on $\left[4,5\right]$?

What is the average value of $f(x)=x^3+2$ on $\left[1,4\right]$?

What is the average value of $f(x)=x^3+2$ on $\left[2,7\right]$?

What is the average value of $f(x)=2x^3$ on $\left[2,7\right]$?

A machine draws current at a rate $i(t)=2t$ amperes for $0\le t\le 6$ seconds. What is the average current over that interval?

What is the average value of $f(x)=9\sin x$ on $\left[0,\pi \right]$, with $x$ in radians?

The function $f(x)=e^x$ is continuous on $\left[1,4\right]$. What does the Mean Value Theorem for Integrals guarantee?

Water flows into a tank at a rate $r(t)=5t$ gallons per minute for $0\le t\le 12$ minutes. What is the average flow rate over that interval?

A car's velocity is $v(t)=3t$ feet per second for $0\le t\le 6$ seconds. What is the average velocity over that interval?

For $f(x)=\sqrt{x}$ on $\left[0,18\right]$, the Mean Value Theorem for Integrals guarantees a $c$ in $\left(0,18\right)$ with $f(c)$ equal to the average value. What is $c$?

A car's velocity is $v(t)=4t^2$ feet per second for $0\le t\le 6$ seconds. What is the average velocity over that interval?

What is the average value of $f(x)=3x^2$ on $\left[1,4\right]$?

For $f(x)=x^2$ on $\left[0,6\right]$, the Mean Value Theorem for Integrals guarantees a $c$ in $\left(0,6\right)$ with $f(c)$ equal to the average value. What is $c$?

What is the average value of $f(x)=6e^{-x}$ on $\left[0,2\right]$?

What is the average value of $f(x)=4e^{-x}$ on $\left[0,1\right]$?

What is the average value of $f(x)=4x^3$ on $\left[2,3\right]$?