Level curves MIT 1802SC Multivariable Calculus, Fall 10Abstract In this chapter we discuss the problems and theorems of the previous chapter using some new terminology The concepts we are going to examine here revolve around functions defined on a plane and their level curvesThese are especially useful in the solutions to problems involving maxima and minimaThe Gradient and the Level Curve Our text does not show this, but the fact that the gradient is orthogonal to the level curve comes up again and again, and in fact, the text proves a more complicated version in three dimensions (the gradient is orthogonal to the level surface) It is important, so we go through a proof and an example
16 1 Functions Of Several Variables
