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

Question

What is the x-coordinate of the point on the curve f (x) = √x (7x - 6) , where the tangent is parallel to x-axis? (A)  - (1/3) (B)  (2/7) (C)  (6/7) (D)  (1/2)

Tardigrade Admin · Accepted Answer

f(x) = √x(7x-6) =7x3/2 - 6x1/2 f'(x) = 7×(3/2) x1/2 - 6 ×(1/2) x-1/2 When tangent is parallel to x axis then f '(x) = 0 or (21/2) x1/2 - 3x-1/2 = 0 or (21/2) √x = (3/√x ) or, 7x =2 ⇒ x = (2/7)

Q. 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?

$- \frac{1}{3}$

$\frac{2}{7}$

$\frac{6}{7}$

$\frac{1}{2}$

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

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

−31​

72​

76​

21​