How do you find a local minimum of a graph using the first derivative?

1 Answer
Jim H
Mar 9, 2018

Please see below.

Explanation:

For the graph of a function, #f(x)#

Find critical numbers for #f#. These are the values in the domain of #f# at which #f'(x) = 0# or #f'(x)# does not exist.

Test each critical number using either the first (or second) derivative test for local extrema.

If #c# is a critical number for #f# and if

#f'(x)# changes from negative to positive as x values move left to right past #c#, then #f(c)# is a local minimum for #f#.

#f'(x)# changes from positive to negative as x values move left to right past #c#, then #f(c)# is a local maximum for #f#.

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