AP Calculus Ab Project

By: Malcolm Brissett

Plz no sleeping

while presentation

is playing

Get Readyshhh Slope field

Consider the differential equation dy/dx = x^4 (y-2)

(a) On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated.(Note: use the axes provided)

(b) while the slope field in part (a) is drawn at only twelve points, it is defined at every point in the xy-plane. Describe all point in the xy-plane for which the slope are negative.

(c) find the particular solution Y= f(x)to the given differential equation with the initial condition F(0)=O.

2004 AP Calculus AB Exam (Form B)

Problem 5

On the axes provided, sketch a slope field for the given differential equation at the twelve points indicated.(Note: use the axes provided)

A.

dy/dx = x^4 (y-2)

(X,Y) dy/dx(0,0) 0(0,1) 0(0,2) 0(0,3) 0(1,0) -2(1,1) -1(1,2) 0(1,3) 1(-1,0) -2(-1,1) -1(-1,2) 0(-1,3) 1

Calculator Part A.1 2

3

Turn on yourcalculators

Then Go to PRGm

Plug in the equation

Then go down to slopefld

6

4 5

Then Go to window set to set it for the points you need

PRESS ENTER

7

LAST.. Go to graph =) and yay your done.

while the slope field in part (a) is drawn at only twelve points, it is defined at every point in the xy-plane. Describe all point in the xy-plane for which the slope are negative.

B.

Because slope at  (x.y) is given by  , slope is negative only where X^4is positive And (y-2 ) is negative.  So slope is negative in 

find the particular solution Y= f(x)to the given differential equation with the initial condition F(0)=O.

C.

Citations

http://rowdy.mscd.edu/~talmanl/APCalculus/AB2004B/

http://apcentral.collegeboard.com/apc/public/repository/ap04_frq_calculus_ab__36107.pdf

1

2

The

END