Min/Max + Lagrange
The critical points of the function f(x,y) = x2+ (y-1)2 ?
What is the point (0,1) ?
The y partial derivative at the point (1,0.5) of the function
f = y*sin-1(xy)
What is 1/sqrt(3) + pi/6 ?
The limit of the function f(x,y) = y5cos(xy + 7) as (x,y) approaches (2,5)
(Don't need decimals)
What is 25cos(17) ?
The unit vector in the direction <4,3>
What is <4/5 , 3/5> ?
The interpretation of the x partial derivative for a function f(x,y) at the point (a,b)
What is the slope of f(x,y) at the point (a,b) in the direction (1,0) ?
Use the second derivative test to determine if the point (3,2) is a max/min or neither if fxx = 4 , fyy = -8 , fxy = -3
What is the point is a saddle point ?
The local max, min, and saddle points of the function
f(x,y) = x3 + y3 - 3x2 - 3y2 - 9x
What are the saddle points (3,0) , (-1,2) , the local maximum (-1,0) , and the local minimum (3,2) ?
The description of the surface x2 + 2z2 = 1
What is a cylinder about the y-axis ?
This is perpendicular to the gradient at the point (a,b)
What is a level curve?
The first partial derivative of f(x,y) = x/y
What is fx = 1/y fy = -x / y2
The process for finding the max/min/saddle points of a function (looking for a long answer)
What is finding the critical points where fx = fy = 0 and then using the second derivative test. If negative, it's a saddle point. If positive, it's a max/min. + fx = min - fx = max ?
The partial derivative dP/dx when P = sqrt(u2+v2+w2) for x = 0 , y = 2
u = xey
v = yex
w = exy
What is 6/sqrt(5) ?
What is a family of planes with the normal vector <1, 3, 5> ?
A vector normal to the graph
f(x,y) = x^3 - 3yx^2 + 6xy^2 - y^3
at the point (1,1,3)
What is < 3, 6, -1>
The expression for the partial derivative dF/dt.
For the function of F(x,y) , where x and y are both functions of s and t,
What is dF/dt = dF/dy * dy/dt + dF/dx * dx/dt ?
The critical points for the function
g(x,y) = 26 − 27x^2 − 18y^2 + y^4
and whether they are min/max/saddle
What is the points saddle (0, -3), max (0,0), and saddle (0,3) ?
The x derivative of the function F = y2*ln(t2 - cos(y)) + tan(ty)
What is 0?
The domain and sketch of the domain of the function ln(9 - x2 - 9y2)
What is the interior of the ellipse x2/9 + y2 < 1 ?
Find the maximum rate of change and the direction in which is occurs for f(x,y,z) = xln(yz) at the point (1,2,1/2)
What is sqrt(17) / 2 in the direction <0, 1/2, 2> ?
The equation of the tangent plane to z = x/y2 at the point (-4,2,-1)
What is z = 1/4 *x + (1/2)y -2 ?
The minimum point and value of the function f(x,y) = x2 + y2
What is (0,0) and 0 ?
Show that every plane tangent to the cone x2 + y2 = z2 passes through the origin
What is :
Cone is a level surface. Gradient is (2x,2y,-2z) is the normal vector. Tangent plane is x0x + yoy - zoz = 0. This always contains the origin
What is a contour map of ellipses with the form x2 + 4y2 = ek ?
The directional derivative of f(x,y,z) = xy2z3 at P(2,1,1) in the direction of Q(0, -3, 5)
What is 1?
Assuming that the equation x^3 + y^3 + z^2 = 0 defines z as a function of the independent variables x and y, find the partial derivatives ∂z/∂x and ∂z/∂y
What is ∂z/∂x = − Fx/Fz= − 3x^2 / 2z and
∂z/∂y = − Fy/Fz = − 3y^2 / 2z ?