Exam 14: Partial Derivatives

Find the differential of the function

Find all the second partial derivatives of

If R is the total resistance of three resistors, connected in parallel, with resistances , then . If the resistances are measured in ohms as , with a possible error of 0.8% in each case, estimate the maximum error in the calculated value of R.

Describe the level survaces of the function .

Find the absolute extrema of the function on the closed triangular region with vertices , and .

Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is

Find the gradient of at the point

Use the Chain Rule to find and if and

Let and suppose that changes from to (a) Compute (b) Compute

Find the critical points of the function.

Use partial derivatives to find the implicit derivative

Find the first partial derivatives of the function

Find the direction in which the function decreases fastest at the point .

Find an equation of the tangent plane to the given surface at the specified point.

Evaluate the gradient of f at the point P.

Find equations for the tangent plane and the normal line to the surface with equation at the point

Find , if and .

Find the equation of the tangent plane to the given surface at the specified point.

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Determine where the function is continuous.