# Derivatives and graphs

## Homework Statement

What is the relationship with a function's rising, falling, high point or low point to it's derivative?

## 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

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?

Much Appreciated

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Mark44
Mentor

## Homework Statement

What is the relationship with a function's rising, falling, high point or low point to it's derivative?
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.

## 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
What graphs are you talking about?
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?
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.

For the acceleration graph, the acceleration is the derivative with respect to time, of the velocity. The same relationships hold as for position and velocity.

I have a graph of f and a graph of f'. That's what I meant by graphs. Sorry if it wasn't clear.

Thanks though!