Modul
e
4
: Local / Global Maximum / Minimum and Curve Sketching
Lecture
11 : Convex / Concave Functions [Section 11.2]
PRACTICE EXERCISES
1.
For the following functions, find the intervals of convexity/ concavity, and points of inflection:
ANSWER
2.(i)
Show that the function
has a critical point at
but not a point of inflection at
(ii)
Show that
has horizontal tangent at
and also
is a point of inflection.
However,
is not a point of inflection, yet at this point
is a tangent to the graph of the function.
(iii)
The function
does not have point of inflection at
. Does it have any point of
inflection?
3.
Show that for
, both the function have critical point at
Show
that for
it is not a point of inflection. What about for
?
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has a critical point at 
but not a point of inflection at 
has horizontal tangent at 
and also 
is a point of inflection. 
is not a point of inflection, yet at this point 
is a tangent to the graph of the function.
does not have point of inflection at 
. Does it have any point of 
, both the function have critical point at 
Show 
it is not a point of inflection. What about for 
? 
