Figure 3.4.2(a) contains an image of the    tutor applied to $f\left(x\right)\=x e^{-x}$ on the interval $\left[0\,3\right]$.

The value of $c\=0.880$ is returned for the point where the tangent line is parallel to the secant line drawn from $\left[0\,f\left(0\right)\right]$ to $\left[3\,f\left(3\right)\right]$.

Amongst the Student packages, only the LinearAlgebra subpackage provides control over the number of digits used by the tutors. In the Mean Value Theorem tutor, the number of digits used for $c$, namely, three, is hard-coded in the tutor.

Type $f\left(x\right)\=\dots$, being sure to use the exponential "$e$".

Context Panel: Assign Function

Write the equation $f\left(b\right)\=f\left(a\right)\+f\prime \left(c\right)\left(b-a\right)$, being sure to put a space between $f\prime \left(c\right)$ and $\left(b-a\right)$. Press the Enter key.

Context Panel: Solve≻Numerically Solve

Figure 3.4.2(b) animates the graph in Figure 3.4.2(a). The slider controls the value of $b$, the right endpoint of the interval $\left[0\,b\right]$.

Click on the graph to access the animation toolbar, in the center of which is a slider that controls the value of $b$.