Use a Graphing Utility to Graph the Function Over the Indicated

question 217

Multiple Choice

Use a graphing utility to graph the function over the indicated interval and approximate any local maxima and local
minima. Determine where the function is increasing and where it is decreasing. If necessary, round answers to two
decimal places.
- $f(x) =x^{3}-3 x+3,(-2,2)$

• A)
• local maximum at \( (1,1) \)
• local minimum at \( (-1,5) \)
• increasing on \( (-2,-1) \)
• decreasing on \( (-1,1) \)
• B) local maximum at \( (-1,5) \)
• local minimum at \( (1,1) \)
• increasing on \( (-2,-1) \) and \( (1,2) \)
• decreasing on \( (-1,1) \)
• C) local maximum at \( (1,1) \)
• local minimum at \( (-1,5) \)
• increasing on \( (-2,-1) \) and \( (1,2) \)
• decreasing on \( (-1,1) \)
• D)
• \(\begin{array}{l}
• \text { local maximum at }(-1,5) \\
• \text { local minimum at }(1,1) \\
• \text { increasing on }(-1,1) \\
• \text { decreasing on }(-2,-1) \text { and }(1,2)
• \end{array}\)

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Definitions:

Pooled Variance Estimate

A method to estimate variance combined from two or more samples that assumes the samples originate from populations with the same variance.

Common Variance

The variance shared by two or more variables, often assessed to understand the relationship or correlation between them.

Weighted Average

An average that multiplies each component by a predetermined weight before calculating the overall average.

Degrees of Freedom

The number of independent values or quantities that can vary in the analysis of data sets, important for determining the significance of statistical tests.