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find the equation of the line that is tangent to x sqrtxy=6 at (4,1)

Mathematics
Tutor: None Selected Time limit: 1 Day

slope and derivative

Oct 2nd, 2014

√(xy) = 6/x

xy      = (6/x)²

xy      = 36/x²

y      = 36/x =36x⁻¹ 

  dy     =- 36 x-² = -36 /x²                                                                                                                                             dx

derivative at (4,1)= -36/4² =-9

Equation of tangent

y - y1=m(x - x1)

y - 1  = -9 (x - 4)

y - 1  = -9 x + 36

     y  = -9 x + 37


Oct 2nd, 2014

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