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AP EAMCET201822 Apr 2018Evening ShiftMathematicsApplication of DerivativesActual

On the curve y=x^3 , the point at which the tangent line is parallel to the chord joining the points (-1,-1) and (2,8) is

Options

  1. A(1, - 1)
  2. B(2, 8)
  3. C(1, 1)
  4. D(3, 27)

Correct answer

C. (1, 1)

Step-by-step solution

According to Lagrange's Mean value theorem, y=x^3 is a continuous and differentiable function So, there exist x= c , such that f^ (c)= f(2)-f(-1) 2-(-1) aligned & & 3 c^2 & = 8-(-1) 3 =3 c^2=1 & & c & = 1 aligned So, point is (1,1) .

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