Exercise 8: Directional Rate of Change
a) Find the rate of change for $z = 4x - 3y + 5$ when we change the $(x, y)$-input in the direction of the vector $(7, -1)$.
b) The linear function $z = \lambda[x, y]$ has gradient $G(5, -7)$ and $\lambda[4, 6] = 7$. Find the rate of change $z$ when we change $(x, y)$ in the direction of the vector $(7, -1)$.