AP Calculus AB
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Transcript of AP Calculus AB
04/19/23 Perkins
AP Calculus AB
Day 2Section 4.1
Sketch the graph of two functions with the derivative shown.
'f x
10
5
-5
-10
-10 10
f x
f x
f ’(x) has 2 zeros
f(x) has 2 horizontal tangents
2. Find a general solution and show a rough graph for y if
2 1dy
xdx
3. Find an equation for y if and y passes through (1,1).
2 1dy
xdx
2 1dy x dx
2 1dy x dx 2 12 1
2 1y x x C 2y x x C
2y x x C 2
1 1 1 C 1 C 2 1y x x
6
4
2
-2
-4
-6
-5 5
Solve the differential equation '' sin if ' 0 1f x x f
and 0 6f
' sinf x x dxcos x C
' 0 cos0f C
1 1 C 2 C ' cos 2f x x
cos 2f x x dx sin 2x x C
0 sin 0 2 0f C
6 0 0 C 6 C
sin 2 6f x x x
Perkins
AP Calculus AB
Day 2Section 4.1
Sketch the graph of two functions with the derivative shown.
'f x
10
5
-5
-10
-10 10
2. Find a general solution and show a rough graph for y if
2 1dy
xdx
3. Find an equation for y if and y passes through (1,1).
2 1dy
xdx
6
4
2
-2
-4
-6
-5 5
Solve the differential equation '' sin if ' 0 1f x x f
and 0 6f