### Home > PC3 > Chapter 13 > Lesson 13.3.4 > Problem13-140

13-140.

If $f\left(x\right)=\sqrt{x}$, then $f'(x)=\frac{1}{2\sqrt{x}}$.

1. Show that the slope of the tangent line to the curve $y=f(x)$ when $x=9$ is $\frac { 1 } { 6 }$.

The slope function is $f'$. Therefore evaluate $f'(9)$.

2. Let $g(x)=10\sqrt{x}$. What is the slope of the tangent line to the curve when $x=9$?

$g$ is a transformation of $f$. It is just scaled by a factor of $10$.
How does this affect the slope?

3. How could you use the results from part (a) to answer the question in part (b)?