Answer :

Given:

There are given the function:

[tex]f(x)=3-x[/tex]

Explanation:

To find the maxima and minima extrema, first, we need to find the difference between the given function:

So,

[tex]\begin{gathered} f(x)=3-x \\ f^{\prime}(x)=-1 \end{gathered}[/tex]

Now,

Since f'(x) exists for all x, the only critical numbers of occure when f'(x) = 0.

Then,

According to the given differentiation, there are no critical points.

That means:

[tex]-1\ne0[/tex]

Now,

The values at the endpoints of the interval, put -1 and 2 into the above function:

[tex]f(-1)=4[/tex]

And,

[tex]\begin{gathered} f(x)=3-x \\ f(2)=3-2 \\ f(2)=1 \end{gathered}[/tex]

Comparing these two numbers, we see the absolute maximum value and the absolute minimum values.

Final answer:

Hence, the minimum and maximum extrema are shown below:

[tex]\begin{gathered} minima:(2,1) \\ maxima:(-1,4) \end{gathered}[/tex]

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