Consider the Cobb-Douglas production function of three variables, $w=f(x, y, z)=C x^{\alpha} y^{\beta} z^{\gamma} .$ Show that $(\mathrm{a})$ $f(d x, d y, d z)=d^{\alpha+\beta+\gamma} f(x, y, z),(\mathrm{b})$ $x f_{x}(x, y, z)+y f_{y}(x, y, z)+z f_{z}(x, y, z)=(\alpha+\beta+\gamma) f(x, y, z)$ (c) in particular, when $\alpha+\beta+\gamma=1,$ give an economic interpretation of these results.