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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