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Questions and Worked Solutions for AP Calculus AB 2015.

5. The figure above shows the graph of f', the derivative of a twice-differentiable function f, on the interval [-3,4]. The graph of f' has horizontal tangents at x = -1, x = 1, and x = 3. The areas of the regions bounded by the x-axis and the graph of f' on the intervals [-2,1] and [1,4] are 9 and 12, respectively.

(a) Find all x-coordinates at which f has a relative maximum. Give a reason for your answer.

(b) On what open intervals contained in -3 < x < 4 is the graph of f both concave down and decreasing?

Give a reason for your answer.

(c) Find the x-coordinates of all points of inflection for the graph of f. Give a reason for your answer.

(d) Given that f(1) = 3, write an expression for f(x) that involves an integral. Find f(4) and f(-2).

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More videos, activities and worksheets that are suitable for Calculus

Questions and Worked Solutions for AP Calculus AB 2015.

AP Calculus AB 2015 Free Response Questions - Complete Paper (pdf)

5. The figure above shows the graph of f', the derivative of a twice-differentiable function f, on the interval [-3,4]. The graph of f' has horizontal tangents at x = -1, x = 1, and x = 3. The areas of the regions bounded by the x-axis and the graph of f' on the intervals [-2,1] and [1,4] are 9 and 12, respectively.

(a) Find all x-coordinates at which f has a relative maximum. Give a reason for your answer.

(b) On what open intervals contained in -3 < x < 4 is the graph of f both concave down and decreasing?

Give a reason for your answer.

(c) Find the x-coordinates of all points of inflection for the graph of f. Give a reason for your answer.

(d) Given that f(1) = 3, write an expression for f(x) that involves an integral. Find f(4) and f(-2).

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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