If $f ^ { \prime \prime } ( x ) = - 4 \sin 2 x , f ( 0 ) = 0 , f ^ { \prime } ( 0 ) = 2$

question 75

Short Answer

If $f ^ { \prime \prime } ( x ) = - 4 \sin 2 x , f ( 0 ) = 0 , f ^ { \prime } ( 0 ) = 2$ , find the value of $f \left( \frac { \pi } { 4 } \right)$ .

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Definitions:

Broca Area

An area located within the dominant hemisphere's frontal lobe (typically the left side) of the brain, responsible for controlling speech generation.

Motor Speech Area

A region of the brain, typically located in the frontal lobe, involved in the planning, control, and execution of voluntary speech.

Cerebral Cortex

The outer layer of neural tissue of the cerebrum in the brain, playing a key role in memory, attention, perception, cognition, awareness, thought, language, and consciousness.

Primary Somatosensory Cortex

The region of the brain responsible for processing sensory information from the body, allowing for the perception of touch, temperature, and pain.