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Warm up 8/24
Estimate the instantaneous
rate of change at x = 3 for the
function f ( x )  x 2  3
Warm up
1.
Do in notebook
by picking values close to 3.
Be seated before the bell rings
DESK
homework
Warm-up (in
your notes)
Agenda :
warm-up
Go over test
Notes lesson 2.1
Notebook
Learning Target
Table of content
Page
1)
1-1 A Preview of
Calculus
1
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
1
AP Calculus AB Learning Targets Chapter 2 part 1
Section
LT1:
2.1
Learning Target
I
Know
It !!
Partially Don’
t
Get It
Get
it
I can use the limit
definition of the
derivative.
HW:
2.1 p 103; 1,2,5,9,13,14,17,20,22,23,25,39-42,45,46,4952
2.1 The Derivative
the slope at 1 pt
Average rate of
Instantaneous ROC
change (ROC)
Slope at instant f ( x )
f
(
x
)
f(b)
f(a)
a
b
f (b)  f (a )
ba
c
???
Find slope at c.
f ( x)
f(X)
f(c)
c X
lim
f ( x )  f (c )
xc
xc
f ( x )  f (c )
lim
x c
xc
(Find the slope of f(x) at x = 3)
ex : f(x) = 2x + 7
f '(3)
2
ex : f(x) = x -3x-2
f ( x )  f (c )
lim
x c
xc
f '(2)
f '(4)
f '(2)
f '( x)
f '( x)  equation for deriv.
f ( x)
f ( x  x)
f(x)

x
x x  x
lim
x  0
lim
h0
f ( x  x)
- f(x)
x
f ( x  h)
h
- f(x)
EX : f ( x)  x  x
2
f '( x)
lim
h0
f ( x  h)
- f(x)
h
f '(3)  7
f '(0)  1
f '(1/ 2)  0
EX : f ( x)  x
f '( x)
dy
Notations: f '( x ) ,
Tangent Lines
dx
d
, y ' ,  f ( x) 
dx
f ( x)  x  3
2
x2
y  y1  m  x  x1 
2
Find equation of tangent line at x = -1
f ( x)  x  x  3
3
2
y  3  1( x  1)