Chapter 13.6, Problem 43E

(a)

To determine

To calculate: The components of the vector in the direction of the maximum rate of increase in the function $f\left(x,y\right)=\frac{1}{10}\left(x^2-3xy+y^2\right)$ at the given point $\left(1,2\right)$ with the help of the graph refer to the diagram provided in the question.

(b)

To determine

To calculate: The gradient of the function $f\left(x,y\right)=\frac{1}{10}\left(x^2-3xy+y^2\right)$ at point $\left(1,2\right)$ and verify with the direction obtained in part (a).

(c)

To determine

The direction in which the rate of function $f\left(x,y\right)=\frac{1}{10}\left(x^2-3xy+y^2\right)$ is decreasing at the faster rate.