# Function, derivatives, error, and stationary points.

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Consider the function of two real variables x and y (y not 1) defined by....

Find the first-order and second-order partial derivatives of f.

Determine the second-order Taylor polynomial for f near (0,-1)

Use first-order partial derivatives to determine the least and greatest possible values.

Use the chain rule to determine, in terms of t, the rate of change of f.

Locate and classify all the stationary points of f.

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##### Solution Summary

This provides a series of problems involving a function, including partial derivatives, second-order Taylor polynomial, least and greatest possible values, maximum possible error, rate of change, and stationary points.

##### Solution Preview

(a) We have the following derivative calculations.

(b) From (a), we can get the second order Taylor polynomial for near the point . We have

(c) We only use the ...

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