CPM Homework Help : PC Problem 9-156

Show that the equation of the tangent line to the curve $y = 12\sqrt { x }$ at the point $\left(4, 24\right)$ is $y = 3x + 12$ .

Hint:

Use the point - slope form for a linear function.
You are given a point. So now you need the slope of the tangent line.

1. Find the slope function at $x = 4$ .
2. Graph the slope function.
3. As $h→0$ , what does the slope approach?

Partial Answer:

$\lim\limits_{ h \to 0}\frac{12\sqrt{4+h}-12\sqrt{4}}{h}$

Use the slider in the eTool below to see that the slope at $x = 4$ is $3$ . Then find the equation of the tangent line with the given point and slope.
Click the link at right for the full version of the eTool: 9-156 HW eTool