Question

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

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

Hint:

Horizontal tangents occur where the first derivative is zero.

Answer 1

The Correct Option is B

Step 1: Tangent parallel to x-axis ⟹ f'(x)=0.
Step 2: Differentiate: f'(x)=\frac12√(x)(7x-6)+7√(x)
Step 3: Set to zero and simplify: frac7x-6+14x2√(x)=0 ⟹ 21x-6=0 ⟹ x=(2)/(7)