Chapter 5 Quiz 2

A visually appealing image depicting concepts of calculus, including graphs of fun<wbr>ctions, derivatives, and concavity, with a classroom setting in the background.

Understanding Derivatives and Concavity: Chapter 5 Quiz

Test your knowledge on derivatives and concavity with this engaging quiz! Covering key concepts from Chapter 5, this quiz will assess your understanding of graphical interpretations and behavior of functions based on their derivatives.

Key Features:

8 multiple choice questions
1 text question
Designed for students and learners of calculus

8 Questions2 MinutesCreated by CalculatingEagle42

The graph of f', the derivative of the function f, is shown above. Which of the following statements must be true?

I. F has a relative minimum at x = -3.

II. The graph of f has a point of inflection at x = -2.

III. The graph of f is concave down fo 0 < x < 4.

The figure above shows the graph of f', the derivative of the function f, for -6 < x < 8.

Of the following, which best describes the graph of f on the same interval?

1 relative max, 1 relative min, and 4 points of inflection.

1 relative minimum, 1 relative maximum, and 3 points of inflection

2 relative minima, 1 relative maximum, and 2 points of inflection.

2 relative minima, 1 relative maximum, and 4 points of inflection.

2 relative minima, 2 relative maxima, and 3 points of inflection.

The graph of f', the derivative of a function f, is shown above. The domain of f is the open interval 0 < x < d. Which of the following statements is true?

F has a local minimum at x = c.

F has a local maximum at x = b.

The graph of f has a point of inflection at (a,f(a)).

The graph of f has a point of inflection at (b,f(b)).

The graph of f is concave up on the interval (c,d).

The graph of f'', the second derivative of the function of f, is shown above. Which of the following could be the graph of f?

Three graphs labeled I, II, and III are shown above. One is the graph of f, one is the graph of f', and one is the graph of f''. Which of the following correctly identifies each of the three graphs.

The graph of f'', the second derivative of f, is shown above for -2 ≤ x ≤ 4. What are all intervals on which the graph of f is concave down?

Chapter 5 Quiz 2

Understanding Derivatives and Concavity: Chapter 5 Quiz

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