Find the first-order partial derivatives of Find all second-order partial deriva

Question

Find the first-order partial derivatives of Find all second-order partial derivatives of f(x, y) = 6 xy3 - 2x3y + x- 6 x2y2 -f 9. For the function given in problem 2. find fyxx. The volume of a right circular cone of radius r and height h is given by V = 1/3 pir2h.Show that alpha v/alpha r = Find any relative extrema and saddle points for the function f(x, y) = 6xy-x3-y3 +7. If the sum of the length /. width h, and height h, of a rectangular crate is 3 m. find the dimensions such that the volume is a maximum.

Explanation / Answer

V = 1/3 * pi * r^2 h

dV / dr = 1/3 * pi * 2r * h = 2/3 * pi * r * h

2V/ r = 2 * 1/3 * pi * r^2 * h / r = 2/3 * pi * r * h

LHS = RHS

Thus the proof

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