Prerequisite concepts The Master Formula The gradient is a vector For an $n-$dimensional function $f$, the gradient of $f$ at a point is an $n-$dimensional vector *The Direction of the Gradient *The Magnitude of the Gradient New prereq concept The Hillside Directional Derivatives New taught by The components of the gradient are partial derivatives FIXME Representations used No activity! NEEDS NAME $\left(\frac{\partial f}{\partial x}\right)_y$ ENTER LONG DESCRIPTION No activity! NEEDS NAME $\vec \nabla f$ ENTER LONG DESCRIPTION New representation The Valley The gradient can tell you a small change in a function in any direction (differentials edition) New needed for concept