The function is and the interval is
.
Construct a table for different values of in the interval
.
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
![]() | \
Observe the table:
\ is positive and
is negative, therefore the value of
changes its sign for
.
By the location principle has a zero between
and
.
is negative and
is positive, therefore the value of
changes its sign for
.
By the location principle has a zero between
and
.
is positive and
is negative, therefore the value of
changes its sign for
.
By the location principle has a zero between
and
.
Graph of the function :
Observe the graph:
\The curve crosses the -axis between
and
;
and
;
and
.
Therefore, the zeros of on
occur between
and
;
and
;
and
.
The zeros of on
occur between
and
;
and
;
and
.