'Hand derivative' diaporamas de présentation

Chapter 3

Chapter 3. Differentiation. 3.1. The Derivative as a Function. The limit when it existed, is called the Derivative if f at x 0 . View derivative as a function derived from f. If f ' exists at x , f is said to be differentiable (has a derivative) at x

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Chapter 3

Chapter 3. Differentiation. 3.1. The Derivative as a Function. The limit when it existed, is called the Derivative if f at x 0 . View derivative as a function derived from f. If f ' exists at x , f is said to be differentiable (has a derivative) at x

1.33k views • 132 slides

2.1 Tangents and Derivatives at a Point

2.1 Tangents and Derivatives at a Point. Finding a Tangent to the Graph of a Function. To find a tangent to an arbitrary curve y=f(x) at a point P(x 0 ,f(x 0 )), we Calculate the slope of the secant through P and a nearby point Q(x 0 +h, f(x 0 +h)).

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2.1 Tangents and Derivatives at a Point

2.1 Tangents and Derivatives at a Point. Finding a Tangent to the Graph of a Function. To find a tangent to an arbitrary curve y=f(x) at a point P(x 0 ,f(x 0 )), we Calculate the slope of the secant through P and a nearby point Q(x 0 +h, f(x 0 +h)).

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Section 2.1: The Derivative and the Tangent Line Problem

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Differentiability, Local Linearity

Differentiability, Local Linearity. Section 3.2a. How f ( a ) Might Fail to Exist. A function will not have a derivative at a point P ( a , f ( a )) where the slopes of the secant lines,. f ail to approach a limit as x approaches a . Four instances w here this occurs:.

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3.1 Derivative of a Function

3.1 Derivative of a Function. In section 2.4, we defined the slope of a curve y = f(x) at the point where x = a to be When it exists, this limit is called the derivative of f at a .

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Definition of the Derivative

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Tangent lines

Tangent lines. Recall: tangent line is the limit of secant line The tangent line to the curve y=f(x) at the point P(a,f(a)) is the line through P with slope provided that the limit exists. Remark. If the limit does not exist, then the curve does not have a tangent line at P(a,f(a)).

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Tangent lines

Tangent lines. Recall: tangent line is the limit of secant line The tangent line to the curve y=f(x) at the point P(a,f(a)) is the line through P with slope provided that the limit exists. Remark. If the limit does not exist, then the curve does not have a tangent line at P(a,f(a)).

151 views • 13 slides