AP EAMCET202318 May 2023Evening ShiftMathematicsApplication of DerivativesActual

The equation of the normal to the curve y= x drawn at the point nearest to the origin is

Options

Ay=0
Bx=1
Cx=0
Dy=1

Correct answer

C. x=0

Step-by-step solution

y= h x y^ = hx To find the nearest point to the origin, we can set the derivative equal to zero. h ( x )=0 The only solution of this equation is x=0 At x=0, y= cash (0)=1 The slope of normal is m = (- 1 y ^1 )_ (0,1) = (- 1 x )_ (0,1) m = -1 0 Now, the equation of the normal is (y-1)=- 1 0 (x-0) (x-0)=0 x=0

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