Let F(x)and G(x)be Two Functions $H ^ { \prime } ( 2 )$

question 53

Short Answer

Let f(x)and g(x)be two functions.Values of f(x), f '(x), g(x), and g'(x)for x = 0, 1, and 2 are given in the table below.Use the information in the table to find $H ^ { \prime } ( 2 )$ if $H ( x ) =$ [f(x)]².
$\begin{array} { c c c c c } \boldsymbol { x } & f ( x ) & f ^ { \prime } ( x ) & g ( x ) & g ^ { \prime } ( x ) \\0 & 1 & - 1 & 2 & 5 \\1 & - 1 & 2 & 4 & 0 \\2 & 7 & 3 & 11 & 0.5\end{array}$

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Definitions:

Reticular Formation

A network of nerve pathways in the brainstem involved in consciousness and alertness.

Brainstem

The lower part of the brain that connects to the spinal cord, controlling fundamental body functions.

Sleep-Wake Cycles

The natural, circadian rhythm-driven pattern of alternating sleep and wakefulness, closely tied to the 24-hour day-night cycle.

Midbrain

A part of the brainstem that plays an important role in motor movement, particularly movements of the eye, and in auditory and visual processing.