Juan Gallegos November 2011. Objective Objective of this presentation 2.
Objective
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WEDNESDAY, OCTOBER 25TH Score 2.8 Lesson 3.2 Reminders “Consider the postage stamp: its usefulness consists in the ability to stick to one thing till it gets there.” ~Josh Billings
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Objective. 10/29 Lesson 3.2. 2. 1. What is the name of the angle pair, angles 1 and 2 ?. What if the lines are parallel?. 2. 1. Handbook page 15. Watch it!. Find m QRS. Write it!. Example 1). 4. 3. m. 8. 1. 7. 2. n. 5. 6. - PowerPoint PPT Presentation
Transcript of Objective
WEDNESDAY, OCTOBER 25TH
Score 2.8Lesson 3.2Reminders
“Consider the postage stamp: its usefulness consists in the ability to stick to one thing till it gets there.” ~Josh Billings
Lesson 3.1 Scoring Guidelines
5 Limit done both ways
7 Slope of secant; is it larger or smaller than f’(2)?
9 Estimate f’(1) and f’(2)
13 Which is larger?
19 Find derivative; then write equation of tangent line
35 Find derivative using limit process
49 Intervals on which derivative is positive
51 Find f(x) and a
56 Find f(x) and a
59 A. B.
Lesson 3.2The Derivative as a Function
Section 3.1, Figure 3Page 102
h
afhafaf
h
)()(lim)('
0
Generalizing for all x …
h
xfhxfxf
h
)()(lim)('
0
Using the definition
23)(for )(' xxfxf xxfxf )(for )('
06
1
232
63
)(')(
23
2
x
xxx
xx
xfxf
The Power rule:
1)( nn xnxdx
d
Ready for a shortcut?
Find each derivative using the power rule.
xy
xy
xxg
xxf
1.4
1.3
2)(.2
)(.1
2
4
xxx
xg
xxf
x
xxxg
ttf
232
)(.8
2
1)(.7
2)(.6
5
4)(.5
34
3 2
3
2
4at 325)(
toline tangent theofequation theFind10.
:derivative theCompute.927
37
axxxf
xdx
d
x
To which of the following does the Power rule apply?
x
x
yc
xxgb
xxfa
2.
)(.
)(. 2
54.
)(.
)(.
xyf
xge
xxfd
x
11. Let
Complete the table below for y’.
xx
y 26
3
6
-6
6 2.5 0 -1.5 -2 2.5-1.5
x -4 -3 -2 -1 0 1 2 3 4
y’ 0 6
The value of the derivative and what it tells me about f(x)
f’(x) is positive
Slope of the tangent line to f is positive
f is increasing at that point
f’(x) is negative
Slope of the tangent line to f is negative
f is decreasing at that point
f’(x) is zero
Slope of the tangent line to f is zero
f has a horizontal tangent line at that
point
The value of the derivative and what it tells me about f(x)
f’(x) is positive
Slope of the tangent line to f is positive
f is increasing at that point
f’(x) is negative
Slope of the tangent line to f is negative
f is decreasing at that point
f’(x) is zero
Slope of the tangent line to f is zero
f has a horizontal tangent line at that
point
Not all functions have a derivative at every single point!
When the limit exists, we say that the function is differentiable at a.
Discontinuity Sharp Turn Vertical Tangent Line
A function is NOT DIFFERENTIABLE if the graph has these characteristics:
