Question

Find an equation of the tangent line is used to find the equation of the tangent line at a given point on a:

A) Line
B) Circle
C) Curve
D) Parabola

Answer 1

The equation of the tangent line is used to find the equation of a tangent line at a given point on a curve or a parabola. You need to determine the point and the slope of the curve at that point, then use the point-slope form to write the equation.

Step-by-step explanation:

The equation of the tangent line is typically used to find the equation of the tangent line at a given point on a curve or a parabola. To find the tangent line, you need to determine a specific point on the curve and the slope of the curve at that point. The slope of the curve at a point is equal to the slope of the tangent line at that point, as demonstrated when you have to find the tangent to the curve at some time value, for instance, t = 25 s.

Here is a step-by-step explanation of how to find the tangent line:

1. Find the specific point on the curve where you need the tangent line, such as at t = 25 s.
2. Determine the endpoints of the tangent. For example, endpoints corresponding to positions at different times can be used.
3. Using these endpoints, calculate the slope of the tangent line using the standard slope formula.
4. Finally, knowing a point on the curve and the slope, use the point-slope form of the line equation to write the equation of the tangent line.

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