How do I find the maximum and minimum values of the function #f(x) = x - 2 sin (x)# on the interval #[-pi/4, pi/2]#?

1 Answer
Gió
Jan 30, 2015

You can derive your function and set your derivative equal to zero. The value(s) of #x# you'll find will be the points of maxima or minima.

In your case you have:

#f'(x)=1-2cos(x)#

Setting #f'(x)=0# gives:

#1-2cos(x)=0#
When #x=pi/3#

You can now analyze when the derivative is bigger than zero:

#1-2cos(x)>0#
i.e. when #x>pi/3#
enter image source here
Your value of #x=pi/3# represent a minimum for your function, and in your interval you get the graph:
enter image source here

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