Module 4 : Local / Global Maximum / Minimum and Curve Sketching
Lecture 12 : Curve sketching [Section 12.2]
(ii)
for .
(iii)
(iv)
is twice differentiable with
(a) .
(b) .
(c).
(d).
(v)
We want to sketch the graph of with the given data. The graph is smooth; continuous; passing through points ; with local maximum at and local minimum at . Further, it is strictly concave down in strictly concave up in with a point of inflection at . It has no asymptotes, decrease to as and increases to as . Thus a graph of is given by:
for 
. 
is twice differentiable with
.
.
.
.
with the given data. The graph is smooth; continuous; passing through points 
; with local maximum at 
and local minimum at 
. Further, it is strictly concave down in 
strictly concave up in 
with a point of inflection at 
. It has no asymptotes, 
decrease to 
as 
and 
increases to 
as 
. Thus a graph of 
is given by:
