ap calculus ab
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AP Calculus AB. Day 9 Section 5.4. Theorem:. 1.Find the slope of the line tangent to f ( x ) at x = 3. 4.Find extrema and inflection points for. Crit #’s:. Crit #’s:. Can’t ever work. none. Intervals:. Test values:. f ’’(test pt). f(x). f ’(test pt). f(x). rel max. rel min. - PowerPoint PPT PresentationTRANSCRIPT
04/19/23 Perkins
AP Calculus AB
Day 9Section 5.4
ude
dx Theorem:
122. x
de
dx
u due
dx
3. lnxde x
dx
1. Find the slope of the line tangent to f (x) at x = 3.
2' 2xf x e 2xf x e 6' 3 2f e
6
2
e
2 32xe x
2xde
dx
123
2xx e
1lnx xe e x
x
1
lnxe xx
1 1ln
xx
e x
1 lnx
x x
xe
4. Find extrema and inflection points for 2 xy x e
2 2x xdyx e e x
dx
20 2 0xe x x Crit #’s:
Can’t ever work.
0,2x
2 2xe x x
2
22
2 2 2x xd ye x e x x
dx
22 2 2xe x x x
2 4 2xe x x Crit #’s:
20 4 2 0xe x x none
24 4 4 1 2
2 1x
4 8
2x
4 2 2
2x
2 2x
2 1.4x
.6,3.4x
Intervals: ,0 0,.6 .6,2
Test values: 1 12 1
f ’(test pt) f(x) dec inc inc
rel min rel max
0x 2x 0,0 2
42,e
f ’’(test pt) f(x) up up down
2,3.4 3.4,3 5
dec dec
down up
2 2xdye x x
dx
22
24 2xd y
e x xdx
2xe x x
Inf pt Inf pt
.6x 3.4x 0.586,0.191 3.414,0.384
2 xy x e
Perkins
AP Calculus AB
Day 9Section 5.4
ude
dx Theorem:
122. x
de
dx
3. lnxde x
dx
1. Find the slope of the line tangent to f (x) at x = 3.
2xf x e
4. Find extrema and inflection points for 2 xy x e
