first derivative test

Question

How do I use the first derivative rule in order to find local and absolute extrema?

Answer 1

After you find the first derivative, set it equal to zero that will give you the potential candiates for absolute extrema. Then construct a sign chart of the first derivative for those numbers where you pick a number less than or between those numbers and then plug them into for x in the first derivative. Solve the equation and see if their sign is positive or negative then. If it is negative then positive it is min. If it is positive then negative it is min. Now that is local extrema to find absolute extrema take the values for the local extrema and plug those into the ORIGINAL EQUATION and find out which one is the biggest and smallest values.

Answer 2

You can also use second derivative test, by finding out the concavity. if f' is + it is concave up which means it is a min, if f' is - then it is concave down which means it is a max. But since your looking for first derivative rule this does not apply.