How do you estimate derivatives when you don't know the actual equation of the line on the graph, but you have just a picture of the graph?
Draw tangent lines and calculate their slopes by checking the x- and y-intercepts.
estimate the slope of the tangentline.
Estimating derivatives from a graph can be done using a visual approach. While it may not provide precise values, it can help you approximate the slope of a curve at a specific point.
To estimate the derivative visually, you can follow these steps:
1. Locate the point on the graph where you want to estimate the derivative. This point is usually denoted by a dot or a labeled point on the curve.
2. Draw a tangent line to the curve at that specific point. A tangent line is a straight line that touches the curve at only one point and represents the instantaneous slope of the curve at that point.
3. Measure the slope of the tangent line. You can do this by comparing the rise (vertical change) and the run (horizontal change) of the line. Find two points on the tangent line, one at the beginning and one at the end, and calculate the difference in the y-coordinate (rise) and the difference in the x-coordinate (run) between those points.
4. Finally, estimate the derivative by dividing the rise (change in y-coordinate) by the run (change in x-coordinate). This ratio represents the approximate slope of the curve at the chosen point.
While this method is not as accurate as finding the derivative algebraically from an equation, it provides a reasonable estimation. Keep in mind that the accuracy of the estimation will depend on the precision of the graph and the chosen points on the tangent line.