If a graph of a function is given and they tell you to draw the derivative, how do you find it if the function is not given.
draw a tangent line and find the slope of that line, the derivative is equal to the slope of a tangent line at the point
If they want you to PLOT the derivative (df/dx), you will have to measure the slope of the tangent line at a series of points along the f(x) curve, and then plot df/dx vs x.
A triangular plate sits on the x−y plane, and has the following vertices:(0,0), (1,0), and (1,2). It's mass-density is given by the function f(x,y)=xy.
If only the graph of a function is given and the function itself is not provided, there are a few ways you can estimate or draw an approximation of its derivative. Here are the steps you can follow:
1. Identify the slope at specific points: Look for points on the graph where the slope appears to be steepest or shallowest. At these points, estimate the slope of the tangent line. The slope can be determined by drawing a small line that is tangent to the curve at that particular point and measuring its gradient.
2. Use the slope to plot derivative points: Once you have estimated the slope for various points on the graph, plot those slopes as points on a new graph. The x-coordinates of the points should correspond to the x-values of the original graph, while the y-coordinates should represent the corresponding slope values.
3. Connect the points with a smooth curve: After plotting the derivative points, connect them smoothly to form the approximate graph of the derivative. Use a curve that matches the trend of the derivative points, considering whether the original function is increasing or decreasing.
It's important to note that this method of estimating the derivative from a graph is not always accurate and may only provide an approximation. The accuracy depends on the clarity and precision of the original graph. Additionally, this approach assumes that the derivative exists at every point on the graph.