4'1 Drawing Rates of Change Graphs

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4.1 Drawing Rates of Change Graphs
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Strategy
To graph a rate of change graph, complete the
following table for each point x where the
function is differentiable.
Plot the points (x, mtan) to produce the rate of
change graph. Note This process can be done
visually as well by estimating the slope of the
tangent lines.
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Slope Graph (x, m)
y -3x 5
y x 7
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Slope Graph (x, m)
(-?, a) m gt 0 m - ? to m? 0 x a m
0 (a, b) m lt 0 m 0 to minimum m to m
0 x b m 0 (b, ?) m gt 0 m 0 to m?to
?
m 0
m lt 0
m gt 0
m gt 0
m gt 0
b
m gt 0
a
m gt 0
m lt 0
m 0
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Examples
Page 243 2 10 even, 16
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4.2 Simple Rate of Change Formulas
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Derivative Formulas
Derivative formulas can be easily calculated
using derivative (rate of change) formulas. This
eliminates the need to use the limit of the
difference quotient discussed in section 3.5.
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Examples
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Derivative Formulas
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Examples
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Examples
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