anonymous
  • anonymous
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.
Mathematics
katieb
  • katieb
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mathteacher1729
  • mathteacher1729
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

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