# How do you use the closed-interval method to find the absolute maximum and minimum values of the function #f(x)=x-2sinx# on the interval #[-π/4, π/2]#?

##### 2 Answers

The answer is:

First of all, let's see if there are some local maximum o minimum in that interval.

So the function grows in

and decreases in

graph{x-2sinx [-4.93, 4.94, -2.465, 2.466]}

So the point

Now we have to calculate the ordinate of both the extremes of the interval, because the absolute maximum and minimum could be in that points.

The points are:

So the absolute maximum is

First of all, let's recall how the method works: if you have a continuous function (which is

So, first of all, let's derive the function: since the derivative of a sum is the sum of the derivatives, you have that

Now, let's recall that we can factor out constants:

These are both elementary derivatives, and we have

This function has zeroes if and only if

The only thing left is thus to compare the values of the function in

Some easy computations show that:

And so the minimum value of