What are the local extrema, if any, of #f(x)= x^2-1#?

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Answer 1 · 2015-12-03T02:07:53

#(0,-1)#

Local extrema occur when #f'(x)=0#. So, find #f'(x)# and set it equal to #0#.

#f'(x)=2x#

#2x=0#

#x=0#

There is a local extremum at #(0,-1)#.

Check a graph:

graph{x^2-1 [-10, 10, -5, 5]}