How do you read a second derivative graph?

This 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.

1. Calculate the second derivative.
2. Substitute the value of x.
3. If f “(x) > 0, the graph is concave upward at that value of x.
4. 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

1. If the slope of f(x) is negative, then the graph of f'(x) will be below the x-axis.
2. If the slope of f(x) is positive, then the graph of f'(x) will be above the x-axis.
3. 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