Question

Find the equation of the tangent line at the given point.

a) Geometry
b) Calculator
c) Trigonometry
d) Differentiation

Answer 1

To find the equation of a tangent line at a given point, use differentiation and follow these steps: determine the endpoints of the tangent, calculate the slope using the formula, and plug the slope and coordinates into the point-slope form.

Step-by-step explanation:

The equation of a tangent line at a given point can be found using differentiation. To find the equation of the tangent line at t = 25 s, follow these steps:

1. Determine the endpoints of the tangent, which correspond to a position of 1,300 m at time 19 s and a position of 3,120 m at time 32 s.
2. Calculate the slope of the tangent line using the formula: slope = (change in y-coordinate) / (change in x-coordinate). In this case, the change in y-coordinate is 3,120 m - 1,300 m and the change in x-coordinate is 32 s - 19 s.
3. Plug the slope and the coordinates of the given point (t = 25 s, y-coordinate = value at t = 25 s) into the point-slope form of a linear equation: (y - y-coordinate) = slope * (x - t). Simplify the equation to get the equation of the tangent line.