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Black Book Advanced Problems in MathematicsMathematicsArea Under Curves

For 0 < r < 1 , let n_r denotes the line that is normal to the curve y = x^r at the point (1, 1) . Let S_r denotes the region in the first quadrant bounded by the curve y = x^r ; the x -axis and the line n_r . Then the value of r that minimizes the area of S_r is:

Options

  1. A1 2
  2. B2 - 1
  3. C2 - 1 2
  4. D2 - 1 2

Correct answer

B. 2 - 1

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