Slope Fields Worksheet Page 4
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8Calculus Maximus
WS 5.2: Slope Fields
dy
18. Consider the differential equation
2
y
4
x
.
dx
(a) The slope field for the differential equation is shown below. Sketch the solution curve that passes
.
through the point
0,1 and sketch the solution curve that goes through the point
0, 1
is a solution to the differential equation. Find this value
(b) There is a value of b for which
y
2
x b
of b. Justify your answer.
.
g
0
0
(c) Let g be the function that satisfies the given differential equation with the initial condition
It appears from the slope field that g has a local maximum at the point
0, 0 . Using the differential
equation, prove analytically that this is so.
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