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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2016 · Mathematics · Application of Derivatives

What is the x -coordinate of the point on the curve f(x)= x (7...

What is the xx -coordinate of the point on the curve f(x)=x(7x−6),f(x)=\sqrt{x}(7 x-6), where the tangent is parallel to x\mathrm{x} -axis?

Options

  1. A−13-\frac{1}{3}
  2. B27\frac{2}{7}
  3. C67\frac{6}{7}
  4. D12\frac{1}{2}

Correct answer

B. 27\frac{2}{7}

Step-by-step solution

f(x)=x(7x−6)=7x3/2−6x1/2f′(x)=7×32x1/2−6×12x−1/2f(x)=\sqrt{x}(7 x-6)=7 x^{3 / 2}-6 x^{1 / 2}f^{\prime}(x)=7 \times \frac{3}{2} x^{1 / 2}-6 \times \frac{1}{2} x^{-1 / 2} When tangent is parallel to xx axis f′(x)=0f^{\prime}(x)=0 or, 212\mathrmx1/2−3\mathrmx−1/2=0212x=3x\quad \frac{21}{2} \mathrmx^{1 / 2}-3 \mathrmx^{-1 / 2}=0\frac{21}{2} \sqrt{x}=\frac{3}{\sqrt{x}} or, 7x=2⇒x=277 x=2 \Rightarrow x=\frac{2}{7}
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