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

  1. Refer to the graph below of f ′(x), the derivative of some function f(x). Homework Help ✎

    1. Where is f(x) increasing? How can you tell?

    2. Approximate the interval on which f(x) is concave up. Justify your conclusion with the graph.

    3. 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?