If $f ( x ) = 6 \cos x + \sin ^ { 2 } x$

question 44

Multiple Choice

If $f ( x ) = 6 \cos x + \sin ^ { 2 } x$ , find $f ^ { \prime } ( x )$ and $f ^ { \prime \prime } ( x )$

• A) \(f ^ { \prime \prime } ( x ) = - 6 \cos ( 2 x ) + 2 \cos ( x )\)
• B) \(f ^ { \prime } ( x ) = - 6 \sin ( x ) + \sin ( 2 x )\)
• C) \(f ^ { \prime } ( x ) = - 6 \sin ( 2 x ) + \sin ( x )\)
• D) \(f ^ { \prime \prime } ( x ) = - 6 \cos ( x ) + 2 \cos ( 2 x )\)
• E) \(f ^ { \prime \prime } ( x ) = - 2 \cos ( 2 x ) + 6 \cos ( x )\)

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Definitions:

Energy Difference

The disparity in the amount of energy between two systems, states, or processes, often relevant in physical and chemical phenomena.

Papillae

Small, nipple-like structures on the tongue where taste buds are located, playing a key role in the sense of taste.

Taste Receptor Cells

Specialized cells located on the taste buds of the tongue, responsible for detecting and responding to different taste stimuli such as sweet, salty, bitter, and sour.

Basic Taste

One of the five sensations detected by the taste buds on the tongue: sweetness, sourness, saltiness, bitterness, and umami.