( ) Graphs of Functions and Their Derivatives

Name: __________________________________
Block: _____________ Date: __________
Graphs of Functions and Their Derivatives
f ( x ) , f ' ( x ) , f '' ( x )
For each of the following identify which graph is that of the function, f ( x ) , and which is that of the
first derivative, f ' ( x ) . Justify your choices by identifying all of the key relationships between the two
graphs.
-----------------------------------------------------------------------------------------------------------------------------Example.
- A relative minimum of f ( x ) occurs at x=B and
x=D
x=B
corresponds to a zero of f ' ( x ) .
f ( x)
x=A
- A relative maximum of f ( x ) occurs at x=D
and corresponds to a zero of f ' ( x ) .
- B and D are critical numbers of f ( x ) where
f '( x) = 0 .
- Relative extrema of f ' ( x ) occur at x=A, C, E
f '( x)
and correspond to Inflection Points of f ( x ) .
- A, C, E are critical numbers of f ' ( x ) where
x=C
x=E
f '' ( x ) = 0 .
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For each of the following identify the graph of f ( x ) , of the first derivative, f ' ( x ) , and the second
derivative f '' ( x ) . Justify your choices by identifying all of the key relationships between the three
graphs.
6.
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