Find the Second Derivative of the Function $$y = \frac { 3 - 2 x ^ { 3 } + x ^ { 5 } } { x ^ { 9 } }$$

question 253

Multiple Choice

Find the second derivative of the function.
- $$y = \frac { 3 - 2 x ^ { 3 } + x ^ { 5 } } { x ^ { 9 } }$$

• A) \(\frac { d ^ { 2 } y } { d x ^ { 2 } } = - \frac { 27 } { x ^ { 10 } } + \frac { 12 } { x ^ { 7 } } - \frac { 4 } { x ^ { 5 } }\)
• B) \(\frac { \mathrm { d } ^ { 2 } y } { d x ^ { 2 } } = \frac { 270 } { x ^ { 11 } } - \frac { 84 } { x ^ { 8 } } + \frac { 20 } { x ^ { 6 } }\)
• C) \(\frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } } = \frac { 27 } { \mathrm { x } ^ { 11 } } + \frac { 12 } { \mathrm { x } ^ { 6 } } - \frac { 4 } { \mathrm { x } ^ { 4 } }\)
• D) \(\frac { \mathrm { d } ^ { 2 } y } { d x ^ { 2 } } = \frac { 270 } { x ^ { 12 } } + \frac { 84 } { x ^ { 5 } } - \frac { 20 } { x ^ { 3 } }\)

---

Definitions:

Demand

The quantity of a product or service that consumers are willing and able to purchase at various prices during a given period.

Cost Data

Information related to the expenses incurred in producing a product or delivering a service.

Price Elasticity of Demand

A measure of the sensitivity of quantity demanded to a change in price, indicating how much the quantity demanded of a good will change when its price changes.

Market Power

The ability of a company or group of companies to manipulate or control prices and total market output.