Question

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

• A. $ - \frac{1}{3}$
• B. $ \frac{2}{7}$
• C. $ \frac{6}{7}$
• D. $ \frac{1}{2}$

Answer 1

Answer: (B)

$f\left(x\right) = \sqrt{x}\left(7x-6\right) =7x^{3/2} - 6x^{1/2} $
$ f'\left(x\right) = 7\times\frac{3}{2} x^{1/2 } - 6 \times\frac{1}{2} x^{-1/2}$
When tangent is parallel to x axis then f '(x) = 0
or $ \frac{21}{2} x^{1/2} - 3x^{-1/2} = 0 $
or $\frac{21}{2} \sqrt{x} = \frac{3}{\sqrt{x} }$
or, $ 7x =2 \Rightarrow x = \frac{2}{7} $