how to find the slope of a tangent line? (2.1)
use the slope of smaller and smaller secant lines to find the slope of tangent line at a given point
To find the slope of a tangent line, you need to follow these steps:
1. Identify the point on the curve where you want to find the slope.
2. Choose another point on the curve that is very close to the point you identified in step 1. This point should be closer to the point you identified than any other point on the curve.
3. Calculate the slope of the line that passes through both points using the formula:
Slope = (y2 – y1) / (x2 – x1)
Where (x1, y1) are the coordinates of the first point, and (x2, y2) are the coordinates of the second point.
4. As the second point gets closer and closer to the first point, the slope of the line passing through them will approach the slope of the tangent line at the point of interest. This is because the tangent line is defined as the limit of the slopes of the secant lines as the distance between the two points approaches zero.
5. Therefore, take the limit of the slope as the second point approaches the first point, and you will have found the slope of the tangent line at the point of interest.
Note: If the curve is given by an equation, you can also find the slope of the tangent line by taking the derivative of the equation at the point of interest.
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