311. When you find the maximum for an optimization problem, why do you need to check the sign of the derivative around the critical points?

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Hello, Please answer the following attached Calculus question correctly. Thank you. 

311. When you find the maximum for an optimization
problem, why do you need to check the sign of the
derivative around the critical points?
Transcribed Image Text:311. When you find the maximum for an optimization problem, why do you need to check the sign of the derivative around the critical points?
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