Section 2'6 Tangents, Velocities and Other Rates of Change

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Section 2.6 Tangents, Velocities and Other Rates
of Change
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We began this course by seeking equations of
tangent lines. This was seen as a progression of
secant lines
P
Q
Q
Q
The red line is the desired tangent line.
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The equation of the tangent line can be
calculated if we know the slope of the tangent
line. The slope of the tangent line is the limit
of the slopes of the secant lines.
Now that we have covered limits thoroughly, we
can investigate this further.
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The line tangent to a curve f(x) at a point (a,
f(a)) will have slope
So lets work some examples...
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Another version of the same formula is also
useful
The tangent line slope formula then becomes
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Two useful formulas from this section for the
slope of the tangent line