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Question:
can we solve all maxima/minima question with second derivative test instead of using first derivative test?
Answer:

There are some cases where the first derivative test fails to give you the maxima and minima of a function.

In those cases, we use second derivative test to find maxima and minima. 

So, first we test first derivative test and if it fails, then we go for second derivative test to find maxima and minima.

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