Control-drag $g\left(x\right)\=\dots$

Context Panel: Assign Function

Write $d\left(x\right)\=\dots$

Context Panel: Assign Function

Figure 3.1.2(a) contains a graph of $d\left(x\right)$, the function giving the distance from the fixed point $\left(3\,10\right)$ to $\left(x\,g\left(x\right)\right)$, the generic point on the graph of $g\left(x\right)$.

The smallest value for $d\left(x\right)$ occurs in the interval $\left[0\,1\/2\right]$.

The minimum distance is slightly less than 3.

The animation in Figure 3.1.2(b) is controlled by the slider that sets the value of the $x$-coordinate of the moving green dot in the figure. This dot marks the point on the graph of $g\left(x\right)$ corresponding to that value of $x$. The black dot marks the fixed point $\left(3\,10\right)$.

The corresponding $y$-coordinate is

Assuming $g\left(x\right)$ and $d\left(x\right)$ have already been defined, write the equation expressing the equality of slopes.

Press the Enter key.

Context Panel: Solve≻
Numerically Solve from point≻$x\=1$

$0.2097141098$

Evaluate $d\left(x\right)$ at $x_{\min }$.
Context Panel: Evaluate and Display Inline