# Derivatives and graphs

1. Oct 3, 2006

### Lprchn

There's a series of questions in my homework that I don't understand how to do. They give a graph of f ', then say, given f(-1)=-3/2, sketch the graph of f on the interval [-2,2]. (with different numbers each time, of course)

How would I graph f?

2. Oct 3, 2006

### Staff: Mentor

If you are given f '(x), that is the derivative, or change in f(x) with respect to x. So given some initial condition f(-1), and given f '(-1), that helps you figure out what the values of f(-2) is and f(0) is, etc. If you have a starting value and you know how much it will change over the upcoming interval, that will tell you the final value. Makes sense?

3. Oct 3, 2006

### Lprchn

I don't understand how you can find the specific values of f at other x values by knowing the value of the function and the derivative at a point. Can you explain that further?

4. Oct 4, 2006

### HallsofIvy

You can't. All they are asking for is a rough sketch showing that f increases where f ' is positive and decreases where f ' is negative. Also the graph should rise faster where f ' is larger (the slope is f ').