(a)
\Motion of particle is .
Find the velocity of particle by applying derivative.
\Therefore the velocity of particle is .
Equate it to zero.
\So the critical numbers are and
.
(b)
\Consider the test intervals to find the interval of increasing and decreasing.
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \Test interval | Test value | Sign of ![]() | Conclusion |
![]() | ![]() | \
| Increasing |
![]() | ![]() | \
| Decreasing |
![]() | ![]() | \
| Increasing |
The sign of the velocity function is positive on the intervals and
.
(c)
\The sign of the velocity function is negative on the intervals .
(d)
\(a) The velocity of particle is .
(b) The sign of the velocity function is positive on the intervals and
.
\
(c) The sign of the velocity function is negative on the intervals .
(d) Velocity function changes its direction at and
.