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AP EAMCET202315 May 2023Morning ShiftMathematicsDifferentiationActual

If f(x)= x+ x , then all the points of the set (x, f(x)) / f^ (x)=0 lie on

Options

  1. Aa circle
  2. Ba straight line
  3. Can ellipse
  4. Da parabola

Correct answer

D. a parabola

Step-by-step solution

f(x)= x+ x (given)...(1) Since f^ (x)=0 aligned & (1+ x) 2 x+ x =0 & x=-1 & x=(2 n+1) , n Z aligned at x=(2 n+1) , aligned & f[(2 n+1) ]= (2 n+1) + (2 n+1) & f[(2 n+1) ]= (2 n+1) (2 n+1) =0 n Z & f(t)= t aligned Which represents a Hyperbola.

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