https://file.aiquickdraw.com/mathbot/file/17272327435411lyz0rdo.jpg

The question asks for an analysis based on a graph. Specifically:

1. Part (a) asks to check all labeled points at which exactly two of the following are zero: \( f(x) \), \( f'(x) \), and \( f''(x) \).
2. Part (b) asks to check all labeled points where both \( f(x) \) and \( f'(x) \) are nonzero and have the same sign.

Could you share the graph that this question references, or describe the points where features like zero-crossings, local maxima, minima, or inflection points occur? This information will help in determining where \( f(x) \), \( f'(x) \), and \( f''(x) \) are zero or nonzero, and how their behavior relates at specific points.

Let me know if you would like further clarifications or explanations.

Use the graph shown to answer the following questions:

(a) Indicate (i.e., check) all labeled points at which exactly two of f(x), f'(x), and f''(x) are zero.
(b) Indicate (i.e., check) all labeled points at which f(x) and f'(x) are both nonzero and of the same sign.

This calculus problem involves identifying critical and inflection points on a graph by analyzing where f(x), f'(x), and f''(x) are zero or nonzero. Learn how to solve problems involving the first and second derivatives of a function, suitable for college-level calculus students.

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