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AP EAMCET202123 Aug 2021Morning ShiftMathematicsApplication of DerivativesActual

The slope of the normal to the curve y= x x^2+1 at x=-4 is

Options

  1. A-289 15
  2. B-15 16
  3. C289 15
  4. D15 16

Correct answer

C. 289 15

Step-by-step solution

Slope of normal =- ( d x d y )_ (x₁, y₁ ) Given curve, y= x 1+x^2 , then aligned d y d x & = (1+x^2 )-x(2 x) (1+x^2 )^2 = 1-x^2 (1+x^2 )^2 - d x d y & =- (1+x^2 )^2 1-x^2 = (1+x^2 )^2 x^2-1 aligned At x=-4 aligned (- d x d y )_ x=-4 & = ((-4)^2+1 )^2 (-4)^2-1 & = (16+1)^2 16-1 = 17^2 15 = 289 15 aligned Slope of normal to curve y= x x^2+1 , at x=-4 is 289 / 15 .

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