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Absolute maximum and minimum

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Find the absolute maximum and absolute minimum values of f on the given interval.

F(x) = sqrt(9-x^2) [-1, 2]

or in other words:

F(x) equals the square root of (9 minus x squared).

The problem is also attached in MS word.

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Solution Summary

The solution shows how to find absolute maximum and minimum of a given function on a specified interval.

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F(x) = sqrt(9-x^2) = (9-x^2)^(1/2)
on the interval [-1,2];

are standard notations for writing this equation out in text form. The ^ means exponent.

To find the absolute max and min we have to:
1) find all extreme (or critical points)
2) check the end points.

Calculate the first derivative.
F'(x) = 1/2 (9 - x^2)^(-1/2) (-2x) = - x / sqrt(9-x^2)
(remember to use the chain ...

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