Find the Second Derivative of the Function $$s = \frac { t ^ { 6 } + 2 t + 6 } { t ^ { 2 } }$$

question 139

Multiple Choice

Find the second derivative of the function.
- $$s = \frac { t ^ { 6 } + 2 t + 6 } { t ^ { 2 } }$$

• A) \(\frac { d ^ { 2 } s } { d t ^ { 2 } } = 12 t ^ { 2 } + \frac { 4 } { t ^ { 3 } } + \frac { 36 } { t ^ { 4 } }\)
• B) \(\frac { \mathrm { d } ^ { 2 } \mathrm {~s} } { \mathrm { dt } ^ { 2 } } = 12 \mathrm { t } ^ { 4 } + \frac { 4 } { \mathrm { t } } + \frac { 36 } { \mathrm { t } ^ { 2 } }\)
• C) \(\frac { \mathrm { d } ^ { 2 } \mathrm {~s} } { d \mathrm { t } ^ { 2 } } = 4 \mathrm { t } ^ { 2 } - \frac { 2 } { \mathrm { t } ^ { 3 } } - \frac { 12 } { \mathrm { t } ^ { 4 } }\)
• D) \(\frac { \mathrm { d } ^ { 2 } \mathrm {~s} } { \mathrm { dt } ^ { 2 } } = 4 \mathrm { t } ^ { 3 } - \frac { 2 } { \mathrm { t } ^ { 2 } } - \frac { 12 } { \mathrm { t } ^ { 3 } }\)

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The maximum amount of air a person can expel from the lungs after a maximum inhalation.

Tidal Volume

The amount of air that is inhaled or exhaled during normal breathing with each respiratory cycle.

Residual Capacity

The amount of air remaining in the lungs after a normal expiration, critical for continuous gas exchange between breathing cycles.