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AP EAMCET202017 Sep 2020Morning ShiftMathematicsApplication of DerivativesActual

The slope of the tangent of the curve [ ( x 31 )^n+ ( y 1209 )^n=2 at (31,1209) ]

Options

  1. A-39
  2. B39
  3. C( 1 39 )
  4. D( -1 39 )

Correct answer

A. -39

Step-by-step solution

( ( x 31 )^n+ ( y 1209 )^n=2 ) On differentiating ( aligned & n x^ n-1 31^n + n y^ n-1 1209^n d y d x =0 & d y d x =- ( n x^ n-1 1209^n n y^ n-1 31^n ) & d y d x =- ( x y )^ n-1 (39^n ) aligned ) Slope of tangent at ((31,1209) ) (=- ( 1 39 )^ n-1 (39)^n=-39 )

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