### Home > PC3 > Chapter 13 > Lesson 13.3.5 > Problem13-154

13-154.

Consider the curve $y=12\sqrt{x}$.

1. For what value of $x$ is the slope of the line tangent to the curve $2$?

$m=\lim \limits_{h\to0}\frac{12\sqrt{x+h}-12\sqrt{x}}{h}$

$m=\lim_{h\to0}\frac{12\sqrt{x+h}-12\sqrt{x}}{h}\cdot\frac{\sqrt{x+h}+\sqrt{x}}{\sqrt{x+h}+\sqrt{x}}$

2. At what point is the line tangent to the curve?

Use your value of $x$ from part (a) to compute the corresponding value of $y$.

3. What is the equation of this tangent line?

This is a line with a slope of $2$, passing through the point you found in part (b).