Question

find the derivative of 1/x. find the equation o the line that is tangent to the graph of the function f(x)=1/x when x=2.

Answer 1

We can use the power rule to find the derivative:
\[\frac{d}{dx}\frac{1}{x}=\frac{d}{dx}x^{-1} \Rightarrow \frac{d}{dx}(-1)x^{-2}=\frac{-1}{x^2}\]

As for finding the tangent to the graph of the function, you want your answer to be in point-slope form. That means you need
1) a point (2, 1/2)
2) a slope (the derivative evaluated at x = 2) or -1/(2)^2 = -1/4.

now just fill those happy details into \[y-y_0=m(x-x_0)\]

Where m is the slope and \[(x_0,y_0)\] is the Point. :)

Hope this helps!

ALSO -- download geogebra so you can graph your results. It's free and works on all operating systems.

http://www.geogebra.org/cms/en/installers