We will start from

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We will start from Chapter 2 Sections 2.1 to 2.8
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Chapter 2 Limits and Derivatives
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Slope and Equation of a line
How to find the slop of a line?
How to find the equation of a line?
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Secant line
Tangent line
What is the difference ??
The word tangent is derived from the Latin word
tangens, which means touching.
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Is it possible that a line could be tangent and
secant in the same time
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Secant line and Tangent line
Tangent line
How to find the slope of these lines ??
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Secant line and Tangent line
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Secant line and Tangent line
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Secant line and Tangent line
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Secant line and Tangent line
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Secant line and Tangent line
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2.1 THE TANGENT PROBLEM
tangent line
Q
2.25
1
1.5
1
1
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2.1 THE TANGENT PROBLEM
tangent line
1
1
1
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2.1 THE TANGENT PROBLEM
tangent line
Q
1.44
1
1.2
1
1
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2.1 THE TANGENT PROBLEM

1.5 (1.5,2.25) 2.5
1.2 (1.2,1.44) 2.2
1.1 (1.2,1.21) 2.1
1.01 (1.01,1.0201) 2.01
1
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2.1 THE TANGENT PROBLEM
X2
1
1
x
1
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2.1 THE TANGENT PROBLEM






secant line
2
3
1.5
2.5
2.1
1.1
1.01
2.01
1.001
2.001
1.0
2.0
tangent line
Slope of the tangent line 2.0
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2.1 THE TANGENT PROBLEM

1 0
1.5 0.5
1.9 0.9
1.99 0.99
1.999 0.999
secant line
1.0
2.0
tangent line
Equation of the tangent line
Slope 2.0
point (1, 1)
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2.1 THE TANGENT PROBLEM

1 0
1.5 0.5
1.9 0.9
1.99 0.99
1.999 0.999
secant line
1.0
2.0
tangent line
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2.1 THE TANGENT PROBLEM
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0.3333 0.5
0.2632 0.9
0.2513 0.99
0.2501 0.999

0.2 1.5
0.2381 1.1
0.2488 1.01
0.2499 1.001