2nd Derivative Test

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2nd Derivative Test : 

2nd Derivative Test

A function has critical points at x=3 and x=7. Use the table below to determine (if possible) whether the function has a local max or a local min at those points. Explain your reasoning. : 

A function has critical points at x=3 and x=7. Use the table below to determine (if possible) whether the function has a local max or a local min at those points. Explain your reasoning. Local Max! Local Min!

A function has a critical point at x=2. Use the number line below to determine (if possible) whether the function has a local max or a local min at x=2. : 

A function has a critical point at x=2. Use the number line below to determine (if possible) whether the function has a local max or a local min at x=2. + - + -1 5 Local Max!

A function has critical points at x=-1, x=0, and x=6. Determine (if possible) whether the function has a local max or a local min at those points. : 

A function has critical points at x=-1, x=0, and x=6. Determine (if possible) whether the function has a local max or a local min at those points. @ x=-1, f’’(x) is… Positive. Thus, we have a local min! @ x=0, f’’(x) is… 0! The 2nd Derivative test can’t help us. @ x=6, f’’(x) is… Positive. Thus, we have a local min!