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

1 Answer
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.