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AP EAMCET20225 Jul 2022Evening ShiftMathematicsApplication of DerivativesActual

If the slope of the line through (0,0) which is tangent to the curve y=x^2+x+16 is m then the value of m-4 is

Options

  1. A9
  2. B10
  3. C12
  4. D13

Correct answer

A. 9

Step-by-step solution

y=x^2+x+16 . d y d x |_ (x 1, y 1) =2 x₁+1 Slope of line is y₁-0 d₁-0 = y₁ x₁ 2 x₁+1= y₁ x₁ 2 x₁^2+x₁=y₁ ...(i) Also, (x₁, y₁ . satisfies the curve: y₁=x^2+x₁+16 ...(ii) Put ii in i 2 x₁^2+x₁=x^2+x₁+16 x₁^2 =16 x= 4 x=4y₁= 16+4+16 m= y₁ x₁ = 36 4 =9

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