When the graph of a function f is rising, the derivative f' will be positive. When the graph of f is falling, f' < 0. At either a high point or a low point x0, f'(x) = 0.kLPantera said:Homework Statement
What is the relationship with a function's rising, falling, high point or low point to it's derivative?
What graphs are you talking about?kLPantera said:The Attempt at a Solution
I have plotted my graphs, I can see that they intersect at the high and low points. But what is the relationship
Assuming that the three graphs show the position, velocity, and acceleration of some particle, think about what I said at the beginning of my reply in relation to the position and velocity graphs.kLPantera said:Also on another note, I was wondering if anyone could tell me. When given 3 graphs, how do you tell which one is acceleration, which is velocity, and which is position?
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is essentially the slope of the tangent line at that point.
Derivatives are used in science to help us understand and analyze the behavior of physical systems. They can help us make predictions about the future behavior of a system, and also provide insight into the underlying mechanisms and relationships between different variables.
A graph is a visual representation of data or a mathematical function. In the context of derivatives, graphs are often used to illustrate the relationship between a function and its derivative. The derivative of a function can be represented as the slope of the tangent line on a graph.
A first-order derivative is the rate of change of a function, while a second-order derivative is the rate of change of the first-order derivative. In other words, the second-order derivative represents the rate of change of the rate of change of a function.
Derivatives and graphs have a wide range of real-world applications, including physics, economics, engineering, and biology. They can be used to model and analyze complex systems, make predictions, and optimize processes.