Question

First find the slope and then an equation of the tangent line to the graph of √x at x = 81.

Answer 1

find the slope by taking the derivative and replacing x by 81

Answer 2

Would the derivative be (1/2)x^(-1/2)?

Answer 3

you get
\[\frac{d}{dx}\sqrt{x}=\frac{1}{2\sqrt{x}}\] so your slope is
\[\frac{1}{18}\]

Answer 4

What's "d"?

Answer 5

yes it is true that you can write
\[\frac{1}{2}x^{-\frac{1}{2}}\] but that form is useless for computing

Answer 6

that just means the derivative. write
\[y=\sqrt{x}\]
\[y'=\frac{1}{2\sqrt{x}}\]

Answer 7

How do I write the equation?

Answer 8

use the "point-slope" formula with
\[m=\frac{1}{18},x_1=81,y_1=9\]

Answer 9

Thanks