Question

Question was provided via image upload.

Explanation:

Identify local extrema coordinates from the graph

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$$

Determine intervals of increase and decrease

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Analyze polynomial degree and leading coefficient

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Answer:

Based on the graph of the polynomial function:

1. Local Extrema:

• Local minima occur at \(x = -6\) with value \(-4\), and at \(x = 1\) with value \(-7\).
• A local maximum occurs at \(x = -3\) with value \(-2\).

1. Increasing and Decreasing Intervals:

• The function is increasing on the intervals \((-6, -3) \cup (1, \infty)\).
• The function is decreasing on the intervals \((-\infty, -6) \cup (-3, 1)\).

1. Degree and Leading Coefficient:

• Since there are 3 local extrema, the polynomial has a minimum degree of 4 (even degree).
• Since both ends of the graph point upwards (\(y \to \infty\) as \(x \to \pm\infty\)), the leading coefficient is positive.