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Directional Derivatives in the Plane

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Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- The next map shows the contours on the area in New York. The tributary streams flow perpendicular to the contour.
- The streams are following paths of steepest descent so the water reach the river as quickly as possible.
- The instantaneous rate of change in a stream’s altitude above sea level has a particular direction.
- In this section why this “downhill” direction is perpendicular to the contours.

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Example

- Any other way to find the equation of the tangent line?

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Example

Chapter 14

14.5 Directional Derivatives and Gradient Vectors

- Exercise 14.5, No. 15.
- Exercise 14.5, No. 22.
- Exercise 14.5, No. 31.
- Homeworks must not be submitted, but there will be a 15-minute short quiz in every lecture, asking 1-2 of the homework problems.
- Next short quiz: Next week, at 17.15.