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| PAGE: 220 | SET: Exercises | PROBLEM: 1 |
(a)
The function 
is increasing for the value of 
between 
to 
and 
to 
.
Hence the function 
is increasing over the interval 
and 
.
(b)
The function is decreasing for the value of between 
to 
and to 
.
Hence the function is decreasing over the interval 
and 
.
(c)
Concave upward :
A graph is said to be concave up at a point, if the tangent line to the graph of the curve lies below the graph of the curve at that point.
The function is concave upward over the interval 
.
(d)
Concave downward :
A graph is said to be concave down at a point, if the tangent line to the graph of the curve lies above the graph of the curve at that point.
The function is concave downward over the interval 
and 
.
(e)
Point of inflection :
Inflection points are the points at which the curve changes where the concavity changes from up to down or down to up.
Observe the graph.
The point of inflection occur at 
.
(a) The function is increasing over the interval 
and .
(b) The function is decreasing over the interval and .
(c) The function is concave upward over the interval 
.
(d) The function is concave downward over the interval 
and .
(e) The point of inflection occur at .
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