Final answer:
To find equations for tangent lines to the curve y = x - 1 / x, differentiate the equation to get the slope at a point, then use the point-slope form of a line with the coordinates of the point of tangency.
Step-by-step explanation:
Finding the Equations of Tangent Lines to a Curve
To find the equations of tangent lines to the curve y = x - 1 / x, you need to first differentiate the equation to find the slope (m) of the tangent. This slope is the derivative of the curve at the point of tangency. Once you have the slope, use the point-slope form of a line, which is y - y1 = m(x - x1), where (x1, y1) is the point of tangency on the curve and m is the slope at that point.
To illustrate this with an example, assume we want to find the tangent line at a specific point, say x = a. We would compute the derivative of the curve y', which gives us the slope at any point x. After finding y'(a), we then use the original curve equation to find the y-coordinate of the point of tangency by substituting x = a. Finally, with (a, y(a)) and y'(a), we can write the equation of the tangent line.
Note that the provided information (260 m/s - 210 m/s) / (51 s - 1.0 s) = 1.0 m/s² appears to be related to physics, specifically to calculating the acceleration between two points in time, and does not directly apply to the process of finding tangent lines in mathematics.