Provide an Appropriate Response $f ( x ) = \left\{ \begin{array} { l l } 7 x & 0 \leq x < 1 \\ 0 & x = 1 \end{array} \right.$

question 118

Essay

Provide an appropriate response.
-The function $f ( x ) = \left\{ \begin{array} { l l } 7 x & 0 \leq x < 1 \\ 0 & x = 1 \end{array} \right.$ is zero at $x = 0$ and $x = 1$ and differentiable on $( 0,1 )$ , but its derivative on $( 0,1 )$ is never zero. Does this example contradict Rolle's Theorem?

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Definitions:

GABA

Gamma-Aminobutyric Acid, a neurotransmitter in the brain that is primarily involved in inhibiting neural activity.

Alcohol

A psychoactive substance commonly found in beverages such as beer, wine, and spirits, known for its intoxicating effects.

Nervous System

The network of nerve cells and fibers that transmits nerve impulses between parts of the body, responsible for regulating and coordinating body activities.

Endorphins

Neurochemicals in the brain that act as natural painkillers and also boost pleasure, creating feelings of well-being.