# How do you read a second derivative graph?

Space and AstronomyThis is read aloud as “the second derivative of f. **If f″(x) is positive on an interval, the graph of y = f(x) is concave up on that interval**. We can say that f is increasing (or decreasing) at an increasing rate. If f″(x) is negative on an interval, the graph of y = f(x) is concave down on that interval.

## What does second derivative test tell you?

Video quote: *When the second derivative is less than zero. It's going to have a negative sign and when it's greater than zero that means it's positive when the second derivative is positive we have a graph that is*

## How do you tell if a graph is concave up or down second derivative?

**We can calculate the second derivative to determine the concavity of the function’s curve at any point.**

- Calculate the second derivative.
- Substitute the value of x.
- If f “(x) > 0, the graph is concave upward at that value of x.
- If f “(x) = 0, the graph may have a point of inflection at that value of x.

## How do you read a derivative graph?

**Derivative Graph Rules**

- If the slope of f(x) is negative, then the graph of f'(x) will be below the x-axis.
- If the slope of f(x) is positive, then the graph of f'(x) will be above the x-axis.
- All relative extrema of f(x) will become x-intercepts of f'(x).

## What does the first and second derivative tell you about a graph?

Video quote: *Okay so something that you'll be dealing with a lot is f double Prime so f double Prime tells you your two things that you just have to keep in mind so f double prime is actually the derivative of F*

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