My Partial Derivatives course https//wwwkristakingmathcom/partialderivativescourseIn this video we're talking about how to sketch the level curves ofProblems Elliptic Paraboloid 1 Compute the gradient of w = x 2 5y 2 Answer ∂w ∂w Vw = , = (2x, 10y) ∂x ∂y 2 Show that Vw is perpendicular to the level curves of w at the points (x 0, 0) Answer At (x 0, 0), Vw = (2x 0, 0) Figure 1 The level curves of w = x 2 5y 2 In general, the level curves of w have equation x 2 5y 2We will sketch level curves corresponding to a couples values, such as $0, 1, 1$ The $z=0$ level set is given by $y^2 x= 0$, or $x = y^2$ This is a parabola in $x$ as a function of $y$
Applet Level Curves Of A Hyperbolic Paraboloid Math Insight
