第二十七單元 切平面.

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1 第二十七單元 切平面

2 Tangent Lines The equation of the tangent line at x=a is

3 Tangent Planes

4 Differentiability (One Variable)

5 Differentiability

6 Differentiability

7 Sufficient Condition for differentiability
All of us are continuous

8 Example

9 Example

10 Graph of f (x)

11 The Direction Vector The direction vector is

12 The Direction Vector The direction vector is

13 Normal Vector

14 The Normal Vector of a Tangent Plane

15 Theorem Z=f (x ,y)

16 Example Plane Equation:

17 Example(continued)

18 Tangent plane to the level surface

19 Tangent Plane

20 Example

21 Example

22 graph

23 單元結語 單變數函數可微分的條件微左導數=右導數，以幾何的角度來看，就是存在一條非鉛直的切線。
雙變數函數可微分的條件就比較複雜了，在此我們提出了可微分的充分條件，以幾何的角度來看，就是切平面的存在性。

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