What are the extrema of #f(x)= x+sinx in [-pi,pi]# ?

1 Answer
charlotte
Nov 5, 2015

Absolute maximum at #pi# and an absolute minimum at #-pi#.

Explanation:

For absolute extrema, we need to find the critical numbers by setting the derivative of the equation equal to 0 and plugging them into the function, and then plug in the endpoints of the interval into the original equation.

  1. Finding the critical numbers
    #f'(x) = 1 + cosx#
    #1 + cosx = 0#
    #cosx = -1#
    #x=pi# <-- critical number
    #f(pi)=pi#

  2. Plug in the endpoints
    #f(-pi)=-pi#
    #f(pi)=pi#

Comparing the three, we find that we have an absolute maximum at #pi# and an absolute minimum at #-pi#.

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