MATH 1920 Lecture Notes - Lecture 14: Level Set, Chain Rule, Unit Vector
25 Sep 2017
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Maximized when cos =1, i. e. , when = 0. So max rate of change of f is the direction of. Min rate of change is in the direction of - Example: (,) =ln find the max rate of change and its direction at. So max rate of change is in the direction of <0, 1> and the rate of change is. So is orthogonal to the level curve at every point (assuming the level direction to curve is differentiable) So we have zero rate of change of f when moving in an orthogonal. Functions of 3 variables vector for the tangent plane. By the same calculation as above for any curve through a point p on the. Level curve =(,,) level surface, we get that is normal to the level surface, so it is a normal. Example: find an equation for the tangent plane to fg =2 at p = (2, 1, 0)fg =2 is a level surface of (,,)=fg.
