Final answer:
To find the points where the tangent is parallel to the y-axis, you need to find the x-values where the derivative is undefined. This occurs when the derivative has a vertical asymptote, which means the function has a vertical tangent at that point.
Step-by-step explanation:
In order to find the points where the tangent is parallel to the y-axis, we need to find the derivative of the function. The derivative represents the slope of the tangent line at any point on the curve. For a function to have a tangent line parallel to the y-axis, the derivative must be undefined at that point. This occurs when the derivative has a vertical asymptote, which means the function has a vertical tangent at that point.
To find these points, you need to find the x-values where the derivative is undefined. Set the derivative equal to infinity and solve for x. The resulting x-values will be the points where the tangent is parallel to the y-axis.
For example, let's say we have the function y = x^2 + 3x + 2. The derivative is dy/dx = 2x + 3. Set dy/dx equal to infinity: 2x + 3 = ∞. Solving for x gives x = -3/2. The point (-3/2, y) is a point on the curve where the tangent is parallel to the y-axis.