Question

Find an equation of the tangent line to the curve.

A) Use the slope-intercept form
B) Apply the parametric form
C) Employ the normal vector
D) Use the point-slope form

Answer 1

To find the equation of the tangent line to a curve, we can use the point-slope form.

Step-by-step explanation:

To find the equation of the tangent line to a curve, we can use the point-slope form. Given the endpoints of the tangent line at two different times, we can determine the slope of the line. Using the slope and a point on the line, we can then write the equation in point-slope form, which can be easily converted to the slope-intercept form.

Answer 2

To find the equation of a tangent line to a curve, we can use the slope-intercept form, the parametric form, the normal vector, or the point-slope form. Each method has its advantages.

Step-by-step explanation:

The question asks us to find an equation of the tangent line to a curve. There are multiple methods we can use:

A) To use the slope-intercept form, we need to find the slope of the tangent line and a point on the line. B) To apply the parametric form, we can use the parametric equations of the curve to find the tangent line's equation. C) To employ the normal vector, we can find the unit normal vector to the curve at the given point and use it to define the tangent line. D) To use the point-slope form, we can find the slope of the tangent line and a point on the line, similar to method A.

Each of these methods has its advantages and may be better suited for different scenarios. It is important to understand the concepts behind each method and choose the one that best fits the problem at hand.