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# Applications of multivariable derivatives

## Tangent planes and local linearization

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What is a tangent planeControlling a plane in spaceComputing a tangent planeLokal lineariseringTangent planesLokal linearisering

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## Optimizing multivariable functions

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Multivariable maxima and minimaSaddle pointsWarm up to the second partial derivative testSecond partial derivative testSecond partial derivative test intuitionSecond partial derivative test example, part 1Second partial derivative test example, part 2

## Optimizing multivariable functions (articles)

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Maxima, minima, and saddle pointsSecond partial derivative testReasoning behind second partial derivative testExamples: Second partial derivative test

## Lagrange multipliers and constrained optimization

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Constrained optimization introductionLagrange multipliers, using tangency to solve constrained optimizationFinishing the intro lagrange multiplier exampleLagrange multiplier example, part 1Lagrange multiplier example, part 2The LagrangianMeaning of the Lagrange multiplierProof for the meaning of Lagrange multipliers

## Constrained optimization (articles)

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Lagrange multipliers, introductionLagrange multipliers, examplesInterpretation of Lagrange multipliers

### Om dette emne

The tools of partial derivatives, the gradient, etc. can be used to optimize and approximate multivariable functions. These are very useful in practice, and to a large extent this is why people study multivariable calculus.