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Tangent Planes and Linear Approximations To find the tangent plane to a surface at a given point. 1. To calculate the total differential of a multivariable function. 2. To determine whether or not a function is differentiable. 3. Goals: Derivation of the Tangent Plane to a Surface at a Point Section 14.4 Tangent Planes and Linear Approximations Page 1

Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

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Page 1: Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

Tangent Planes and Linear Approximations

To find the tangent plane to a surface at a given point.1.To calculate the total differential of a multivariable function.2.To determine whether or not a function is differentiable.3.

Goals:

Derivation of the Tangent Plane to a Surface at a Point

Section 14.4 Tangent Planes and Linear Approximations Page 1

Page 2: Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

Section 14.4 Tangent Planes and Linear Approximations Page 2

Page 3: Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

Definitions

Section 14.4 Tangent Planes and Linear Approximations Page 3

Page 4: Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

Section 14.4 Tangent Planes and Linear Approximations Page 4

CChamberlin
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Page 5: Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

Section 14.4 Tangent Planes and Linear Approximations Page 5

Page 6: Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

So, just because the partials exist at a point does not mean that the function is well-behaved at that point.

Section 14.4 Tangent Planes and Linear Approximations Page 6

Page 7: Tangent Planes and Linear Approximations 205...Tangent Planes and Linear Approximations 1. To find the tangent plane to a surface at a given point. 2. To calculate the total differential

Section 14.4 Tangent Planes and Linear Approximations Page 7