There are two special types of functions that deserve special mention. Much like lines play an important role in one variable calculus-after all, the derivative is defined in terms of the tangent line-linear functions also play a special role in multivariable calculus. It shouldn't surprise you to learn that we will define derivatives of multivariable functions in terms of these linear functions. Quadratic functions play a special role in trying to optimize functions of many variables. If we are close enough to an extreme point of a function, the function appears to be one of several ``archetypal'' quadratic functions.