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(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 number is .
(b)
Consider the test intervals to find the interval of increasing and decreasing.
Test interval | Test value | Sign of | Conclusion |
|
Increasing | ||
|
Decreasing |
The sign of the velocity function is positive on the intervals .
(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 .
(c) The sign of the velocity function is negative on the intervals .
(d) Velocity function changes its direction at .
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