Chapter 15.5, Problem 3QC

In Example 1, evaluate D_‒u f(3, 2) and D_−v f(3, 2).

Example 1 Computing directional derivatives

Consider the paraboloid z = f(x, y) = $\frac{1}{4}\left(x^2+2y^2\right)+2$. Let P₀ be the point (3, 2) and consider the unit vectors

u = $\langle \frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\rangle$ and v = $\langle \frac{1}{2},-\frac{\sqrt{3}}{2}\rangle$

a. Find the directional derivative of f at P₀ in the directions of u and v.