Slope Fields Worksheet With Answers - Calculus Maximus, Ws 5.2 Page 4
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8WS 5.2: Slope Fields
Calculus Maximus
WS 7.1: 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 − .
( )
(
)
(b) There is a value of b for which
y
2
x b
+ is a solution to the differential equation. Find this value
=
of b. Justify your answer.
(c) Let g be the function that satisfies the given differential equation with the initial condition
g
0
= .
0
( )
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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