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Describe the behavior of the function in the interval [-\ extinf, -1], including its concavity and monotonicity.
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Step-by-step solution
4 stepsAnalyze the given graph in the interval .
Observe the shape of the curve for values from negative infinity up to .
Determine the concavity of the function in this interval.
In the interval , the graph of the function is curved downwards, resembling an inverted U-shape. This indicates that the function is concave down (مقعرة نحو الأسفل). The inflection point appears to be at .
Determine the monotonicity of the function in this interval.
In the interval , the function is decreasing from to approximately (where it reaches a local minimum), and then it is increasing from approximately to . Therefore, the function is neither strictly increasing nor strictly decreasing over the entire interval .
Compare with the given options.
- مقعرة نحو الأعلى (Concave up): Incorrect, the graph is concave down.
- مقعرة نحو الأسفل (Concave down): Correct, the graph is concave down in this interval.
- تزايدية (Increasing): Incorrect, the function is decreasing then increasing.
- تناقصية (Decreasing): Incorrect, the function is decreasing then increasing.
The correct description for the function in the interval is that it is concave down.
The final answer is
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