Suppose that r(t) = g(t)i + h(t)j + k(t)k is a smooth curve in the domain of a differentiable function (x, y, z). Describe the

Suppose that r(t) = g(t)i + h(t)j + k(t)k is a smooth curve in the domain of a differentiable function ƒ(x, y, z). Describe the relation between dƒ / dt, ∇ƒ, and v = dr/dt. What can be said about ∇ƒ and v at interior points of the curve where ƒ has extreme values relative to its other values on the curve? Give reasons for your answer.