04/19/23 Perkins

AP Calculus AB

Day 4Section 3.3

Find the extrema and sketch 4

2

1xf x

x

3' 2 2f x x x Critical numbers:

3 0x 42 2 0x 4 1x 0x

1x

VA at x = 0

Intervals: , 1 10, 0,1 1,Test values: 3 1

2 12 3

f ’(test pt) f(x) dec inc dec inc

smooth

V.A.

rel min V.A. rel min

1x 0x 1x

1 2f

1 2f

1,2 1,2

2 2x x

3

22x

x

4

3

2 2x

x

4

2

-2

-4

-5 5

4

2

1xf x

x

Given: ' 0 on ( , 2)f x

' 0 on ( 2, )f x

Fill in the appropriate inequality:

2 3q x f x ' 4 0q

4m x f x ' 4 0m

f is decreasing

f is increasing

Move f up 3 and stretch by 2 q is still increasing

Move f up 4 and flip vertically m is decreasing

Perkins

AP Calculus AB

Day 4Section 3.3

Find the extrema and sketch 4

2

1xf x

x

4

2

-2

-4

-5 5

4

2

1xf x

x

Given: ' 0 on ( , 2)f x

' 0 on ( 2, )f x

Fill in the appropriate inequality:

2 3q x f x ' 4 0q

4m x f x ' 4 0m