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Chapter 14Partial Derivatives

0114.01Functions of Multiple Variables
0214.02Limits and Continuity
0314.03Partial Derivatives
0414.04Higher-Order Partial Derivatives
0514.05Tangent Planes and Linear Approximation
0614.06The Chain Rule
0714.07Directional Derivatives
0814.08The Gradient
0914.09Divergence and Curl
1014.10Relative Extrema
1114.11Absolute Extrema
1214.12Lagrange Multipliers

Chapter 14 · Partial Derivatives

0114.01Functions of Multiple Variables
0214.02Limits and Continuity
0314.03Partial Derivatives
0414.04Higher-Order Partial Derivatives
0514.05Tangent Planes and Linear Approximation
0614.06The Chain Rule
0714.07Directional Derivatives
0814.08The Gradient
0914.09Divergence and Curl
1014.10Relative Extrema
1114.11Absolute Extrema
1214.12Lagrange Multipliers

Topics / 14 Partial Derivatives

14.05

Tangent Planes and Linear Approximation

Near a point, a smooth surface looks like a plane. Use that plane to approximate values and small changes.

About 15 minutes

You'll learn to

→Find the tangent plane to z = f(x, y)
→Approximate values with the linearization
→Estimate changes with the total differential

← 14.04 Higher-Order Partial Derivatives 14.06 The Chain Rule →

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