Calculus 4.2

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Mean Value Theorem for Derivatives
Teddy Roosevelt National Park, North Dakota
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Mean Value Theorem for Derivatives
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Mean Value Theorem for Derivatives
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Tangent parallel to chord.
Slope of tangent
Slope of chord
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A couple of somewhat obvious definitions
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These two functions have the same slope at any
value of x.
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Example 6
Find the function whose derivative is
and whose graph passes through
.
so
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Example 6
Find the function whose derivative is
and whose graph passes through
.
so
Notice that we had to have initial values to
determine the value of C.
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The process of finding the original function from
the derivative is so important that it has a name
You will hear much more about antiderivatives in
the future.
This section is just an introduction.