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Calculus 3: Optimization

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All Calculus 33D SpaceVector FunctionsDot and cross productEquations of lines and planesParametric curves, conic sectionsTangent vectors and arc lengthCylinders and quadric surfacesIntegrals of vector functionsArc length and curvatureMultivariable functionsSurface parameterizationPartial derivativesLinearization, chain rule, gradientTangent planes and linear approximationsOptimizationLagrange multipliersDouble integralsTriple integralsChanging coordinates for integrationSurface areaVector fields, divergence, and curlLine integralsGreen's TheoremFluxStokes' TheoremDivergence TheoremComplex numbers
Identifying Critical Points in a Multivariable Function

Given that f(x,y)=10−3x2−2y2+8y+12xf(x, y) = 10 - 3x^2 - 2y^2 + 8y + 12x, identify any critical points, saddle points, and any local extrema.

OptimizationMediumVideo
Critical Points of a Bivariate Quartic Function

Find and classify the critical points of f(x,y)=2x4+2y4−8xy+12f(x,y) = 2x^4 + 2y^4 - 8xy + 12.

OptimizationMediumVideo
Finding Absolute Extreme Values of a Function

Given the function f(x,y)f(x, y) on the rectangle D, find the absolute extreme values.

OptimizationMediumVideo
Wire Cut Optimization for Minimum and Maximum Area

A wire of length 100 centimeters is cut into two pieces; one is bent to form a square, and the other is bent to form an equilateral triangle. Where should the cut be made if (a) the sum of the two areas is to be a minimum; (b) a maximum? (Allow the possibility of no cut.)

OptimizationMediumVideo
Local Extrema Using Second Derivative Test

Find the local extrema of the function f(x,y)=x3−12xy+8y3f(x, y) = x^3 - 12xy + 8y^3 using the second derivative test.

OptimizationMediumVideo