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AP EAMCET202318 May 2023Evening ShiftMathematicsApplication of DerivativesActual

Let n (0, ) . If all the curves y = x ^ n x for distinct values of n , always have y=x-1 as the tangent drawn at a fixed point ( , ) , then + =

Options

  1. A0
  2. B2
  3. C1
  4. D3

Correct answer

C. 1

Step-by-step solution

y=x^n x for n=1, y=x x d y d x = x+1 y = x -1 is tangent line for curve (i) also. x+1=1 x =0 x =1 Now, y = x -1=1-1=0 The fixed point is (x, y) (1,0) ( , )=(1,0) Now, + =1+0=1 .

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