## Related questions with answers

Question

State the complete definition of Second Derivative Test. Under what circumstances is it inconclusive? What do you do if it fails?

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Solution B

Answered 7 months ago

Answered 7 months ago

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1 of 2The second derivative test is a test to see whether the critical point is a maximum or a minimum. If the first derivative is equal to 0, then we check the second derivative at that point and if it is positive then it is a maximum and if it is negative then it is a minimum point. the test fails if the second derivative is equal to 0, because then we dont have a maximum or a minimum, but rather a point of inflection. If this happens we have to check the third derivative to see what the point is on the graph.

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