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| PAGE: 228 | SET: Exercises | PROBLEM: 7 |
(a)
Determine inflection points.
Inflection points are the points at which the curve changes where the concavity changes from up to down or down to up.
The inflection points occurs at the graph changes its concavity.
Observe the graph.
The graph of the curve changes its concavity at 
and 
.
The inflection points occur at and .
(b)
If the graph is of the first derivative then the local minimum or maximum will be the inflection points, since the inflection points occurs where the second derivative will be zero.
Observe the graph.
has inflection points at 
, 
and 
.
(c)
The inflection points occurs where the second derivative will be zero.
Observe the graph.
At 
, the graph 
changes its sign from negative to positive.
At 
, the graph changes its sign from positive to negative.
The inflection points occurs at 
and 
.
(a) 
has inflection points at 
and 
.
(b) has injection points at 
, 
and 
.
(c) has inflection points at and .
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