Question

Does the curve 7x+3y²−y=3 have a vertical tangent line?

A) Yes, it has a vertical tangent line.
B) No, it does not have a vertical tangent line.

Answer 1

The curve 7x+3y²−y=3 has a vertical tangent line at the point (3/7, 0).

Step-by-step explanation:

To determine if the curve 7x+3y²−y=3 has a vertical tangent line, we need to check if the derivative of y with respect to x is undefined at any point on the curve. The derivative of y with respect to x is given by:

dy/dx = -(7/6x + 1/(2y))

A vertical tangent line occurs when the derivative is undefined. To find when the derivative is undefined, we set the denominator equal to zero:

2y = 0

y = 0

Substituting y = 0 back into the original equation, we get:

7x - y = 3

7x - 0 = 3

7x = 3

x = 3/7

So, the curve has a vertical tangent line at the point (3/7, 0).

Therefore, the answer is: A) Yes, it has a vertical tangent line.