What are the extrema of #f(x)= x+sinx in [pi,pi]# ?
1 Answer
Nov 5, 2015
Answer:
Absolute maximum at
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.

Finding the critical numbers
#f'(x) = 1 + cosx#
#1 + cosx = 0#
#cosx = 1#
#x=pi# < critical number
#f(pi)=pi# 
Plug in the endpoints
#f(pi)=pi#
#f(pi)=pi#
Comparing the three, we find that we have an absolute maximum at