The Gradient is perpendicular to level sets, Real Analysis II

In this video, we examine how the gradient is situated in the domain of a scalar-valued function of multiple variables, and demonstrate how it is used to determine tangent lines and planes. We explain how the gradient of a function (say, f) is a vector in the domain which is perpendicular to the level sets of f. We then use this insight to construct tangent approximations for both function and, more generally, graphs of equations (which are not functions). #mathematics #math #realanalysis #gradient #vectorcalculus #MultivariableCalculus #TangentPlane #DifferentialCalculus #calculus3