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BITSAT2016MathematicsApplication of DerivativesActual

What is the x -coordinate of the point on the curve f(x)= x (7 x-6), where the tangent is parallel to x -axis?

Options

  1. A- 1 3
  2. B2 7
  3. C6 7
  4. D1 2

Correct answer

B. 2 7

Step-by-step solution

f(x)= x (7 x-6)=7 x^ 3 / 2 -6 x^ 1 / 2 f^ (x)=7 3 2 x^ 1 / 2 -6 1 2 x^ -1 / 2 When tangent is parallel to x axis f^ (x)=0 or, 21 2 x ^ 1 / 2 -3 x ^ -1 / 2 =0 21 2 x = 3 x or, 7 x=2 x= 2 7

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