Min/Max
The discriminant
What is fxx fyy - fxy2 ?
Relationship between grad f and level curves in a contour plot
What is orthogonal?
The basic Lagrange Multiplier equation
What is
grad f = lambda grad g ?
lim_(k->0) (f(a, b + k) - f(a, b))/k
What is fy ?
grad(fg) = fgradg + ggrad f
What is the Product Rule for Gradients ?
It equals 0 at critical points in 3D
What is the gradient ?
This points in the direction of maximum rate of increase of f(x, y)
What is
grad f ?
The relationship between grad f and grad g when f is maximized
What is parallel ?
What is fx ?
grad(F(f(x,y,z))=F'(f(x,y,z)grad f
What is the Chain Rule for Gradients ?
Discriminant > 0 and fxx < 0
What is a maximum ?
grad f cdot vec u , where vec u is a unit vector
What is the directional derivative Duf ?
The relationship between grad f and the constraint curve g when f is maximized
What is orthogonal ?
Clairaut's Theorem
What is:
(del^2f)/(del x del y) = (del^2f)/(del y del x) ?
If P is a point on the surface F(x, y, z) = k, the relationship between grad F(P) and the surface
What is orthogonal ?
Discriminant > 0 and fxx > 0
What is a minimum ?
Formula for Duf that includes the angle between direction vector vec u and grad f
What is
|| grad f || cos theta ?
When solving a problem, the next step after finding grad f and grad g
What is: solve both equations for
lambda ?
If z = e^(-x^2-y^2) fx =
What is
-2xe^(-x^2-y^2) ?
If f(x, y) = cos(x2 + y), grad F =
What is <(-2x)(sin(x2 + y), -sin(x2 + y)> ?
Discriminant < 0
What is a saddle point ?
The relationship between Duf(P) and the angle of inclination psi
What is
tan psi = Duf(P) ?
When solving a problem, the next step after finding a relationship between x and y
What is: substitute the relationship between x and y into the constraint equation ?
If f(u, v) = cos(u + v2), fuuv =
What is: fuuv = 2v sin(u + v2) ?
d/dtf(r(t))=gradf cdot r'(t)
What is the Chain Rule for Paths ?