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KCET2021MathematicsApplication of Derivatives

If the parametric equation of curve is given by x= + 2 and y= , then the points for which d y d x =0 are given by

Options

  1. A= n 2 , n Z
  2. B=(2 n+1) 2 , n Z
  3. C=(2 n+1) , n Z
  4. D=n , n z

Correct answer

D. =n , n z

Step-by-step solution

x= + 2 Oñ đifferrēñtiāting ̄ w.r.t. , wē gẹt d x d =- + 1 2 ² 2 1 2 aligned &=- + 1 &= 1- ² &= ² ...(i) aligned Now, y= On differentiating w.r.t. , d y d = ...(ii) aligned d y d x &= d y d d x d &= ² = aligned [from Eqs. (i) and (ii)] If d y d x =0 , then =0 . Hence, =n , n Z .

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