Evaluate the indicated derivative at the point (1,2) and write the equation for the tangent line in slope-intercept form?

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  • Vaman
    Lv 7
    1 month ago

    1/y +1/x=2

    Take the derivative.

    -1/y^2 dy/dx-1/x^2=0

    dy/dx= -y^2/x^2, at x=1, y=2, the slope=-4

    The equation is

    y= -4x +c

    This is the solution.

  • 1 month ago

    You have not "indicated" any particular derivative, but I'll assume what's wanted is dy/dx.

    1/y + 1/x = 2 =>

    1/y = 2 - 1/x = (2x - 1)/x =>

    y = x/(2x - 1) =>

    dy/dx = [(2x - 1)*1 - (x)(2)] / (2x-1)^2

    = -1/(2x - 1)^2

    The point (1,2) is not on the given curve, so the meaning of the question is rather mysterious.  Maybe they want a tangent from (1,2) TO the curve?  But no, that doesn't work either, as any line through (1,2) will cross the given curve.

    Either your teacher is a moron or you have miscopied the question.

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