L24 Math 233 Lecture Notes - Lecture 20: Maxima And Minima, Nissan L Engine, Determinant
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L24 math 233 lecture 20- maxima and minima. Equations for different types of 3d shapes for level curves of equations with 3 variables. Ax+by+cz+d is a plane x2 + y2 + z2 = k x2 + y2 = r2. X2 + y2 = z is a sphere with no constraint on z is a cylinder is a cone. Definition- (a,b) is a local maximum for f(x,y) if f (a, ) F (x, ) y for all x,y near a,b. Near a,b means within some small disk centered at a,b. Note: the similarity with local maxima for functions of one variable. Uses the same formula but without y and b and an interval instead of a disk. Note: local maxima and minima are not the same as global maxima and minima. F(x,y) may have a local maximum at a,b which is not the biggest value (global max) The same holds true for a local minimum.
