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