CPM Homework Help : PC3 Problem 13-114

Use the definition of instantaneous rate of change to 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:

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

Step:

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