Question

In Exercises 10-15, a point A is shown on a contour diagram of a function f(x, y).

(a) Evaluate f(A).

(b) Is fₓ(A) positive, negative, or zero?

(c) Is fᵧ(A) positive, negative, or zero?

Answer 1

(a) The value of f(A) is not provided.

(b)
`fₓ(A) and (c) fᵧ(A)` are not provided.

Step-by-step explanation:

In order to evaluate
`f(A), fₓ(A), and fᵧ(A)`, we would need specific numerical values and the contour diagram itself. Unfortunately, without this information, it is impossible to provide the precise values for f(A),
`fₓ(A), and fᵧ(A)`. Contour diagrams typically represent a function's behavior across different levels, and the values at a specific point (A) would be required for accurate computation.

To calculate fₓ(A) and fᵧ(A), the partial derivatives of the function f(x, y) with respect to x and y would need to be determined. These partial derivatives would provide information about the rate of change of the function concerning each variable at the point A. If fₓ(A) is positive, it indicates that the function is increasing concerning the x-variable at point A. Similarly, if fᵧ(A) is positive, the function is increasing concerning the y-variable at point A. Conversely, negative values imply a decrease, and zero implies no change.

In summary, without the specific values or the contour diagram, it is not possible to provide numerical answers for f(A), fₓ(A), and fᵧ(A). The calculation of these values would require the function definition and the ability to evaluate it at point A.