Warm up 8/24

Warm up

1.

Do in notebook

Estimate the instantaneous rate of change at x = 3 for the function

by picking values close to 3.

2( ) 3f x x

Be seated before the bell rings

DESK

homeworkWarm-up (in your notes)

Agenda : warm-upGo over test

Notes lesson 2.1

NotebookTable of content

Page1

Learning Target 1

1) 1-1 A Preview of Calculus

2) 1-2 Finding limits graphically and numerically

3) 1-3 Evaluating limits analytically

4) 1-4 Continuity

5) 1-5 & 3.5

6) 2.1 The Derivative

Section Learning Target I Know It !!

PartiallyGet It

Don’t

Get it

LT1: 2.1 I can use the limit definition of the derivative.

AP Calculus AB Learning Targets Chapter 2 part 1

HW: 2.1 p 103; 1,2,5,9,13,14,17,20,22,23,25,39-42,45,46,49-52

2.1 The Derivative the slope at 1 pt

Average rate of change (ROC)

Instantaneous ROC

( )f x

a b

f(b)

f(a)

( )f x

c

( ) ( )f b f a

b a

???

Slope at instant

( )f x

c

Find slope at c.

X

f(X)f(c) lim ( ) ( )f x f c

x cx c

: f(x) = 2x + 7ex

'(3)f (Find the slope of f(x) at x = 3)

( ) ( )limx c

f x f c

x c

2: f(x) = x -3x-2ex

'(2)f

( ) ( )limx c

f x f c

x c

'(4)f '( 2)f '( )f x

'( )f x equation for deriv.

( )f x

x

f(x)

x

x x

( )f x x lim0x

( )f x x - f(x)

x

lim0h

( )f x h - f(x)

h

2: ( )EX f x x x '( )f x

lim0h

( )f x h - f(x)

h

'(3)f '(0)f

'(1/ 2)f

7

1

0

: ( )EX f x x '( )f x

Notations: '( )f x ,dy dx, 'y , ( )

df x

dx

Tangent Lines 2( ) 3f x x 2x

2

1 1y y m x x

3 2( ) 3f x x x Find equation of tangent line at x = -1

3 1( 1)y x