Definition of the Derivative Using Average Rate (Page 129 - 133 and 160 in the book)

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Definition of the Derivative Using Average
Rate(Page 129 - 133 and 160 in the book)
f(ah)
Slope of the line
Average Rate of Change
f(ah) f(a)
f(a)
h
h
a
ah
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Now, Watch what happens whenPoint a is fixed
and the size of the interval h shrinks
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As h shrinks and approaches zero (but not 0),
the line becomes a Tangent Line
As h approaches zero
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lim Limit, as h approaches zero
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Solution Using the definition
f (x h) -2(x h) 3
(-2x - 2h 3)
-2
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Solution Using the definition
f (x h) (x h)2 - 8(x h) 9
(x2 2xh h2 - 8x -8h 9)
2x - 8