Calculus 6'1

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6.1 Antiderivatives and Slope Fields
Greg Kelly, Hanford High School, Richland,
Washington
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First, a little review
It doesnt matter whether the constant was 3 or
-5, since when we take the derivative the
constant disappears.
However, when we try to reverse the operation
We dont know what the constant is, so we put C
in the answer to remind us that there might have
been a constant.
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If we have some more information we can find C.
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Initial value problems and differential equations
can be illustrated with a slope field.
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0
0
0
0
1
0
0
0
2
0
0
3
2
1
0
1
1
2
2
0
4
-1
-2
0
0
-4
-2
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If you know an initial condition, such as (1,-2),
you can sketch the curve.
By following the slope field, you get a rough
picture of what the curve looks like.
In this case, it is a parabola.
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For more challenging differential equations, we
will use the calculator to draw the slope field.

• Run the program Slope2.
• Enter the equation, using alpha y to enter the y.
• Select xmin, xmax, ymin, and ymax for the desired
  window.

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TA DAH!
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