The height (in feet) attained by a rocket t sec into flight is given by the function .

When is the rocket rising and when is it descending?

A) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 25.
B) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 41.
C) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 65.
D) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 28.

Question

The height (in feet) attained by a rocket t sec into flight is given by the function ​  .
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When is the rocket rising and when is it descending?
​
A) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 25. 
B) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 41. 
C) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 65. 
D) The rocket is rising on the interval and it is descending on the interval where t is some positive number more than 28.

Quizplus · Accepted Answer

To determine when the rocket is rising and when it is descending, we need to examine the derivative of the given function, which represents the rocket's velocity. Taking the derivative of the given function, we get: v(t) = 5t^2 - 60t + 100 The rocket is rising when its velocity is positive, meaning v(t) > 0. To solve for when this is true, we set the velocity function equal to zero and find its roots: 5t^2 - 60t + 100 = 0 t = 6, t = 10 We now have two critical values: t = 6 and t = 10. We can use these values to determine the intervals in which the rocket is rising and descending. When t < 6 or t > 10, the velocity is positive, so the rocket is rising. When 6 < t < 10, the velocity is negative, so the rocket is descending. Looking at the answer choices, we can see that only choice B correctly identifies the intervals in which the rocket is rising and descending. Specifically, the rocket is rising on the interval (0, 6) U (10, ∞) and descending on the interval (6, 10).

The Height (In Feet) Attained by a Rocket T Sec