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AP EAMCET202420 May 2024Evening ShiftMathematicsApplication of DerivativesActual

The length of the subnormal at any point on the curve y= ( x 2024 )^k is constant if the value of k is

Options

  1. A1
  2. B1 3
  3. C1 2
  4. D0

Correct answer

C. 1 2

Step-by-step solution

y= ( x 2024 )^k Differentiating w.r.t. x d y d x = k (2024)^k x^ k-1 Length of subnormal is |y d y d x |= k x^ 2 k-1 (2024)^ 2 k = constant Independent of x and y 2 k-1=0 k= 1 2

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