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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
 10 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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