Answer the following Discussion Question When determining the absolute max and min of a function on a closed interval, i

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Answer the following Discussion Question
When determining the absolute max and min of a function on a closed interval, is the first derivative test necessary? Discuss why/why not.
Does y = (x-5)^(2/3) have a point of inflection? Discuss.
Explain and sketch how a function can have f ''(a) = 0 at (a, f(a)) and not be an inflection point.
Explain and sketch how a function may have two consecutive positive intervals in a first derivative test.
Is y = x^5 - x^2 an example of the 'second derivative test fails'? Discuss.