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KCET2007MathematicsApplication of Derivatives

The point on the curve y²=x , the tangent at which makes an angle 45^ with X -axis is

Options

  1. A( 1 4 , 1 2 )
  2. B( 1 2 , 1 4 )
  3. C( 1 2 , -1 2 )
  4. D( 1 2 , 1 2 )

Correct answer

A. ( 1 4 , 1 2 )

Step-by-step solution

Given, y²=x aligned & 2 y d y d x =1 & d y d x = 1 2 y = Slope aligned Also given, =45^ Slope 45^ =1 1 2 y +1 y= 1 2 From Eq. (i), if y= 1 2 , then x= 1 4 Required point is ( 1 4 , 1 2 ) .

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