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# Calc III

What is the Chain rule for partial derivatives? dz/dt= (dz/dx)*(dx/dt)+(dz/dy)*(dy/dt)
How do you find the domain of a multi-variable function? Find any points at which f(x,y) is undefined and put it in the form x+y>0
What does the partial derivative of a function represent? the slope of the tangent plane, and instantaneous rate of change.
How do you find the best dimensions for a box? write out what you know. xyz=32 Sub out the Z variable. Using this new information make an equation for the quantity that your trying to optimize.
How do you find the tangent plane to a function? Z=Z0+fx(X0,Y0)(X-X0)+fy(X0,Y0)(Y-Y0)
How do you find the gradient vector? del f(X0,Y0)=fx(X0,Y0)I + fy(X0,Y0)J
How do you find the directional derivative? del f . unit vector
How do you find a unit vector? A/|A|
How do you find the local maxs and mins in higher dimensions? Find the critical points, (fx=0,fy=0), find f''(x,y)if its negative then its concave down meaning there's a maximum value, if its positive then its concave up meaning there's a minimum value.
How do you find D using the second order partial test?? |fxx fxy| |fxy fyy|
How do you apply the second order partial test? -if D>0 and fxx>0 then theres a local min@(X0,Y0) -if D>0 and fxx<0 then theres a local max@(X0,Y0) -if D<0 then theres no extreme value and its a saddle point.
Created by: crxingit