Find the Second Derivative of the Function $$y = \frac { x ^ { 4 } + 9 } { x ^ { 2 } }$$

question 70

Multiple Choice

Find the second derivative of the function.
- $$y = \frac { x ^ { 4 } + 9 } { x ^ { 2 } }$$

• A) \(\frac { d ^ { 2 } y } { d x ^ { 2 } } = 2 + \frac { 54 } { x ^ { 4 } }\)
• B) \(\frac { d ^ { 2 } y } { d x ^ { 2 } } = 2 - \frac { 54 } { x ^ { 4 } }\)
• C) \(\frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } ^ { 2 } } = 2 \mathrm { x } - \frac { 18 } { \mathrm { x } ^ { 3 } }\)
• D) \(\frac { \mathrm { d } ^ { 2 } \mathrm { y } } { \mathrm { dx } \mathrm { x } ^ { 2 } } = 1 + \frac { 54 } { \mathrm { x } ^ { 4 } }\)

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Definitions:

Glenoid Cavity

A shallow depression in the scapula that articulates with the head of the humerus to form the shoulder joint.

Sternoclavicular Joint

The articulation between the sternum and the clavicle bone, being a primary connection between the upper limb and the thoracic skeleton.

Acromioclavicular Joint

A joint at the top of the shoulder, where the acromion (part of the scapula) meets the clavicle (collarbone), facilitating shoulder movement.

Coracoid Process

A small hook-like structure on the lateral edge of the superior anterior portion of the scapula (shoulder blade).