Final answer:
To find the equation of a tangent line at a given point using a calculator, you need to find the point of tangency, calculate the slope of the tangent using endpoints, and apply the point-slope formula to formulate the equation.
Step-by-step explanation:
To find the equation of a tangent line at a given point using a calculator, you can follow these steps:
- Determine the point at which you need the tangent line. For example, at t = 25 seconds.
- Identify the endpoints of the tangent on the curve. These could correspond to positions on the curve such as 1300 m at 19 s and 3120 m at 32 s.
- Use the endpoints to calculate the slope (v) of the tangent line. This can be done by subtracting the y-coordinates and dividing by the difference in x-coordinates, following the slope formula (slope = (y2 - y1) / (x2 - x1)).
- Once you have the slope, use the point-slope formula (y - y1) = m(x - x1), where (x1, y1) is the point on the curve and m is the slope, to write the equation of the tangent line.
- Input this data into a calculator or computer to determine the precise equation of the tangent line. If necessary, round off to four decimal places.
Remember to make sure your calculator or software is set to the correct mode (e.g., degrees or radians for trigonometric functions) to come up with an accurate equation of the tangent line.