Question

Sketch the gradient vectorfor the functionwhose level curves are shown. Explain how you chose the direction and length of this vector.

Short answer

The answer is not given in drive.

Step-by-step solution

The gradient vector

The gradient vector perpendicular to the level curves. So draw the parallel line to the level curves and perpendicular line to that line.

The length of gradient

Consider the point and place the starting point of the gradient vector at the point .

The gradient vector perpendicular to the level curves. So draw the parallel line to the level curves and perpendicular line to that line at .

To compute length as follows,

From the given question, the line intersects the contour lines in between and .

The distance is $0.5$ units.

Thus, the length is computed by average rate of change in the direction of the gradient vector.

The length is approximately,

Thus, the length of the gradient vector approximately 2 .

The graph of the gradient vector as shown below in Figure.

From Figure, it can be observed that the length of gradient vector is and it is equal to the maximum value of the directional derivative of .