Find the descending directions at (2,1) for the following functions:

To find the descending directions at a point \((x_0, y_0)\) for a function \(f(x, y)\), we need to compute the gradient \(\nabla f(x, y)\) at that point. The direction in which the function decreases the fastest is opposite to the gradient direction, which is \(-\nabla f(x, y)\).

However, since you haven't provided the specific functions, I can't compute the exact directions for you. Could you please provide the functions you're referring to?

Once I have the functions, I can proceed with calculating the gradient and identifying the descending directions at the point \((2, 1)\).

Would you like to upload the functions or type them directly?

Learn how to find the descending directions at the point (2, 1) for different functions in vector calculus. Explore the gradient concept and directional derivatives to understand how functions decrease at specific points.

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