Show:
Level Curves, Directional Derivatives
Partial Derivatives and Laplace's Theorem
Tangent Planes and Linear Approximations
The Chain Rule
Finding Extrema and Lagrange Multipliers
100

The curve of points (x,y) where f(x,y) is some constant value.

What is a level curve?

100

A planes that touches the surface at the point and is “parallel” to the surface at the point

What is a tangent plane?
100

A function of summation of products of derivatives.

What is the multivariable chain rule?

100

A point where the slopes in orthogonal directions are all zero, but which is not local extremum of the function.

What is a saddle point?

200

The instantaneous rate of change of the function in the direction v through x

What is the directional derivative?

200

fxy=fyx

What is clairaut's theorem?

200

Apply chain rule to the following functions: z=x^2y^3, x=scost, y=ssint

  • (2xy^3)(cost)+(3x^2y^2)(sint)

  • (2xy^3)(-ssint)+(3x^2y^2)(scost)