Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=\sqrt{x}$ on $\left[0,4\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=x^2-5x$ on $\left[-4,4\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=x^2+7x$ on $\left[-5,5\right]$.

A car travels $180$ miles in $3$ hours along a straight road, and its position is a differentiable function of time. What does the Mean Value Theorem guarantee?

Find the value of $c$ the Mean Value Theorem guarantees for $u(x)=x^2-4x$ on $\left[2,8\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=x^2+4x$ on $\left[0,6\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=\frac{1}{x}$ on $\left[1,4\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=\sqrt{x}$ on $\left[0,9\right]$.

A student writes: $g$ is a polynomial on $\left[0,4\right]$, so the Mean Value Theorem guarantees exactly one $c$ where the instantaneous rate equals the average rate. Which best evaluates the argument?

Does the Mean Value Theorem apply to $f(x)=\frac{1}{x+4}$ on $\left[-6,-2\right]$?

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=\sin x$ on $\left[0,\pi \right]$, with $x$ in radians.

A car travels $104$ miles in $2$ hours along a straight road, and its position is a differentiable function of time. What does the Mean Value Theorem guarantee?

A car travels $156$ miles in $3$ hours along a straight road, and its position is a differentiable function of time. What does the Mean Value Theorem guarantee?

Does the Mean Value Theorem apply to $f(x)=\frac{1}{x-2}$ on $\left[0,4\right]$?

Does the Mean Value Theorem apply to $f(x)=x^2+5x$ on $\left[0,4\right]$?

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=x^2+3x$ on $\left[1,7\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=x^3$ on $\left[-1,1\right]$.

Does the Mean Value Theorem apply to $f(x)=x^2+3x$ on $\left[0,4\right]$?

Find the value of $c$ the Mean Value Theorem guarantees for $r(x)=x^2-7x$ on $\left[-5,3\right]$.

A car travels $320$ miles in $4$ hours along a straight road, and its position is a differentiable function of time. What does the Mean Value Theorem guarantee?

Does the Mean Value Theorem apply to $f(x)=\frac{1}{x+1}$ on $\left[-3,1\right]$?

Does the Mean Value Theorem apply to $f(x)=\left|x-2\right|$ on $\left[0,4\right]$?

A student writes: $g$ is a polynomial with $g(0)=2$ and $g(7)=9$, so the Mean Value Theorem guarantees a $c$ in $\left(0,7\right)$ with $g^{\prime }\left(c\right)=0$. Which best evaluates the argument?

Find the value of $c$ the Mean Value Theorem guarantees for $p(x)=x^2+5x$ on $\left[-6,8\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $g(x)=x^2+9x$ on $\left[-5,3\right]$.

Find the value of $c$ the Mean Value Theorem guarantees for $p(x)=x^2+6x$ on $\left[-2,4\right]$.

A student writes: since $f(0)=0$ and $f(8)=8$, the Mean Value Theorem gives a $c$ with $f^{\prime }\left(c\right)=1$. Which best evaluates the argument?

A car travels $156$ miles in $2$ hours along a straight road, and its position is a differentiable function of time. What does the Mean Value Theorem guarantee?

Find the value of $c$ the Mean Value Theorem guarantees for $f(x)=\ln x$ on $\left[1,e\right]$.

A car travels $435$ miles in $5$ hours along a straight road, and its position is a differentiable function of time. What does the Mean Value Theorem guarantee?