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