Find the Equation of the Tangent Line To $f ( x ) = e ^ { - 2 x }$

question 22

Short Answer

Find the equation of the tangent line to $f ( x ) = e ^ { - 2 x }$ at x = 3 and use it to approximate the value of f(3.2).Round to 5 decimal places.

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Definitions:

Hypothalamatic System

A part of the brain responsible for the regulation of certain metabolic processes and other activities of the autonomic nervous system, including temperature regulation, hunger, and thirst.

Growth Spurt

A rapid increase in physical growth, often occurring during puberty.

Pituitary Gland

A small, pea-sized gland located at the base of the brain, known as the "master gland," it plays a crucial role in regulating vital body functions and hormones.

Hypothalamus

A region of the brain that plays a central role in controlling hunger, thirst, sleep, body temperature, and other autonomic nervous system functions.