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. \(-\dfrac{1}{3}\)
• B. \(\dfrac{2}{7}\)
• C. \(\dfrac{6}{7}\)
• D. (1)/(2)

Hint:

Horizontal tangent ⟹ f'(x)=0.

Answer 1

The Correct Option is C

Tangent parallel to x-axis ⟹ f'(x)=0. Differentiating: f'(x)=\frac7x-62√(x)+7√(x) Setting f'(x)=0: 7x-6+14x=0 ⟹ 21x=6 ⟹ x=(6)/(7)