Question

Determine the signs of the partial derivatives for the function\(f\)whose graph is shown.

1. \({{\bf{f}}_{\bf{x}}}( - {\bf{1}},{\bf{2}})\) (b)\({{\bf{f}}_{\bf{y}}}( - {\bf{1}},{\bf{2}})\)
2. \({{\bf{f}}_{{\bf{xx}}}}( - {\bf{1}},{\bf{2}})\) (d)\({{\bf{f}}_{{\bf{yy}}}}( - {\bf{1}},{\bf{2}})\)

Short answer

By using graph determine the signs of the partial derivatives for the function\(f\)

1. \({f_x}( - 1,2)\) (b) \({f_y}( - 1,2)\)

(c) \({f_{xx}}( - 1,2)\) (d) \({f_{yy}}( - 1,2)\)

Step-by-step solution

Given data:

Determine the signs of the partial derivatives for the function \(f\)

Consider the following limit:

The exponential function is continuous everywhere.

The cosine function is continuous everywhere. The product of continuous function is continuous. The given function is continuous everywhere.

Hence, the given limit isexists and equal to.