NOTES Section 3.1 Day 2 The Derivative as a Function Example A · NOTES Section 3.1 Day 2 The...

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NOTES Section 3.1 Day 2 The Derivative as a Function Example A: The graph of a function f is given. Use it to sketch the graph of the derivative, f’. Remember: The derivative at each point on this graph represents So our plan will be: f Axl r l I I r 4 3 y fi x μ t

Transcript of NOTES Section 3.1 Day 2 The Derivative as a Function Example A · NOTES Section 3.1 Day 2 The...

Page 1: NOTES Section 3.1 Day 2 The Derivative as a Function Example A · NOTES Section 3.1 Day 2 The Derivative as a Function Example A: The graph of a function f is given. Use it to sketch

NOTES Section 3.1 Day 2 The Derivative as a Function

Example A: The graph of a function f is given. Use it to sketch the graph of the derivative, f’.

Remember: The derivative at each point on this graph represents So our plan will be:

f Axlr

l I Ir 4

3

y fi x

µ

t

Page 2: NOTES Section 3.1 Day 2 The Derivative as a Function Example A · NOTES Section 3.1 Day 2 The Derivative as a Function Example A: The graph of a function f is given. Use it to sketch

Example B: a) If , find a formula for b) Illustrate by using a graphing device to compare the graphs of and .

b)

Example C: If , find and interpret

xxxf -= 3)( )(' xf

)(xf )(' xf

xxxf -= 3)( )('' xf

f6th Cxth ith

x3t3 h2t3x2hth3 X h

f x Mo t3xh2t3x2hyh3fx h

thing 3xh2t3x2hth3hhnYo 3xht3x2th2 I f G 3 2 1

fW z µr

flcxthl 3CLthJ l3x2t6xht3h2 I

f x Iim t6xht3hn2t3 x

NO f x _x3 xTim lexht3h2 f G 3 2 1

f G LexMO h r

Hymn 6xt3h lf

h n


11 x1 t16 06 derivative times function

11 x1 t16 06 derivative times function

DERIVATIVE OF A FUNCTION 1.5. DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,

DERIVATIVE OF A FUNCTION 1.5. DEFINITION OF A DERIVATIVE OTHER FORMS: OPERATOR:,,,

Lecture 14: The Derivative as a Function

Lecture 14: The Derivative as a Function

Section 2.8 The Derivative as a Function Goals Goals View the derivative f ´(x) as a function of x View the derivative f ´(x) as a function of x Study.

Section 2.8 The Derivative as a Function Goals Goals View the derivative f ´(x) as a function of x View the derivative f ´(x) as a function of x Study.

CHAPTER The Derivative of a Function

CHAPTER The Derivative of a Function

Lesson 9: The Derivative as a function

Lesson 9: The Derivative as a function

The Derivative Function Objective: To define and use the derivative function.

The Derivative Function Objective: To define and use the derivative function.

The Derivative Function

The Derivative Function

3.2 Derivative as a Function

3.2 Derivative as a Function

Chapter Three 0471661740... · 2020. 3. 13. · 142 Chapter Three SHOR T›CUTS O DIFFERENTIATION 3.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS The derivative of a function at

Chapter Three 0471661740... · 2020. 3. 13. · 142 Chapter Three SHOR T›CUTS O DIFFERENTIATION 3.1 DERIVATIVE FORMULAS FOR POWERS AND POLYNOMIALS The derivative of a function at

4.5 Integration by Substitution Outside Function Inside Function Derivative of Inside Function.

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3.1 Definition of the Derivative - University of - Penn Mathdeturck/m103/rogawski/chap3odd.pdf · 3.1 Definition of the Derivative ... In Questions 3–5, f (x) is an arbitrary

3.1 Definition of the Derivative - University of - Penn Mathdeturck/m103/rogawski/chap3odd.pdf · 3.1 Definition of the Derivative ... In Questions 3–5, f (x) is an arbitrary

3.1 limit definition of the derivative

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Warm up Problem If, find.. The Derivative Function Def. For any function f (x), we can find the derivative function f (x) by:

Warm up Problem If, find.. The Derivative Function Def. For any function f (x), we can find the derivative function f (x) by:

3.1 Derivative of a Function What youll learn Definition of a derivative Notation Relationships between the graphs of f and f Graphing the derivative from.

3.1 Derivative of a Function What youll learn Definition of a derivative Notation Relationships between the graphs of f and f Graphing the derivative from.

3.1 Derivative of a Function Objectives Students will be able to: 1)Calculate slopes and derivatives using the definition of the derivative 2)Graph f’

3.1 Derivative of a Function Objectives Students will be able to: 1)Calculate slopes and derivatives using the definition of the derivative 2)Graph f’

DERIVATIVES 3. 3.2 The Derivative as a Function DERIVATIVES In this section, we will learn about: The derivative of a function f.

DERIVATIVES 3. 3.2 The Derivative as a Function DERIVATIVES In this section, we will learn about: The derivative of a function f.

Lesson 9: The Derivative as a Function

Lesson 9: The Derivative as a Function

The Derivative-Instantaneous rate of change The derivative of a function, f at a specific value of x, say a is a value given by: The derivative of a function,

The Derivative-Instantaneous rate of change The derivative of a function, f at a specific value of x, say a is a value given by: The derivative of a function,

The Derivative and Discretionary-Function Immunities of ...

The Derivative and Discretionary-Function Immunities of ...