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anonymous
 one year ago
I was just watching session 2 Clip 2, where the professor solves for the area of the triangle formed by any tangent line to y = 1/x and the y and xaxes. While he finds the xintercept of the tangent in a straightforward manner, using the equation y  y0 = (1/(x0)^2) * (x  x0), from the fact that the derivative of y = 1/x is y = 1/x0^2, making the equation of a tangent line to y = 1/x at some point (x0,y0) what I listed above in pointslope form. But when finding the yintercept, he takes a shortcut using the fact that y = 1/x is its own inverse function. Can anyone explain this shortcut
anonymous
 one year ago
I was just watching session 2 Clip 2, where the professor solves for the area of the triangle formed by any tangent line to y = 1/x and the y and xaxes. While he finds the xintercept of the tangent in a straightforward manner, using the equation y  y0 = (1/(x0)^2) * (x  x0), from the fact that the derivative of y = 1/x is y = 1/x0^2, making the equation of a tangent line to y = 1/x at some point (x0,y0) what I listed above in pointslope form. But when finding the yintercept, he takes a shortcut using the fact that y = 1/x is its own inverse function. Can anyone explain this shortcut

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phi
 one year ago
Best ResponseYou've already chosen the best response.0If you rename x to y and y to x, you end up with the same form of equation, and that equation will have the same value for its intercept (but for x).

anonymous
 8 months ago
Best ResponseYou've already chosen the best response.0Let me use an example in physics to explain inverse function: We know a formula that converts F temperature to C temperature C = 5/9 (F32) To find C, what we do is subtract 32 from F and then multiply by 5/9. To find F, we have to reverse the process. Multiply C by 9/5 and then add 32. Therefore, F = (9/5 * C) +32 Similarly, the inverse function of y = 1/x is x =1/y (replacing y with x and x with y) Now, you know the equation of the tangent line as y1/xo = 1/xo^2 (xxo) Interchange x and y, xo and yo Plugging the value y=0, you get y = 2yo In simple words, if y= 1/x you get x=2xo. If x = 1/y you get y = 2yo Hope you understand this.
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