If you are given a graph of a function, how do you draw the derivative?
You measure the slope of the graph, then graph the slope.
http://people.hofstra.edu/stefan_waner/Realworld/calctopic1/derivgraph.html
Break the graph up into a bunch of increments, each with the same x-axis distance between them. The more the graph flips from up to down, the more increments you need. (The more you have, the better your derivative graph will be.) Write down the (x,y) coordinates of each point. Find the slope between each set of points by taking the rise/run: (y2-y1)/(x2-x1). Plot these points directly between each division you made before. As an example, suppose you initially broke the graph up at each whole number (x=1, x=2, x=3 etc) then your derivative points need to go at x=1.5, x=2.5, x=3.5 etc. Connect these points with a smooth line, and you're done.
To draw the derivative of a function from its graph, you can follow these steps:
1. Understand the concept: The derivative of a function represents its rate of change. It describes how the function is growing or shrinking at any given point. For example, if the derivative is positive, the function is increasing, while a negative derivative indicates a decreasing function.
2. Identify key points: Look for points on the graph where the function shows significant changes in behavior. These points can be peaks, valleys, or any places where the slope seems to change abruptly.
3. Determine tangent lines: At each of the identified points, draw a tangent line that touches the graph of the function at only one point. The tangent line should roughly represent the slope of the function at that specific point.
4. Analyze the tangent lines: Observe the slopes of the tangent lines you drew. If the function is increasing, the slopes should be positive. If it is decreasing, the slopes should be negative.
5. Sketch the derivative: Connect the endpoints of the tangent lines you drew in step 3 using a smooth curve. This curve represents the graph of the derivative.
It is important to note that drawing the derivative from a graph alone may not provide a precise result. To obtain a more accurate depiction of the derivative, it is recommended to use calculus techniques such as finding the limit of the difference quotient or using derivative rules and formulas.