### Home > CALC > Chapter 4 > Lesson 4.3.2 > Problem 4-112

4-112.

Refer to the graph below of

*f*′(*x*), the derivative of some function*f*(*x*). Homework Help ✎

Where is

*f*(*x*) increasing? How can you tell?Approximate the interval on which

*f*(*x*) is concave up. Justify your conclusion with the graph.Is

*f*′′(0) positive or negative? Explain how you know.

Notice that this is the graph of *f* '(*x*), the slopes of *f*(*x*), and *f*(*x*) will increase where its slopes are positive.

*f* ''(*x*) represents the slopes of the given graph, *f* '(*x*). So look at the graph. Does it have a positive or a negative slope at *x* = 0?