Use Rolle's Theorem to Show That F(x) = 4x³

question 69

Essay

Use Rolle's Theorem to show that f(x) = 4x³ + 5x - 1 does not have more than one real root.

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Definitions:

Imaginal Exposure

A cognitive behavioral therapy technique where individuals are asked to vividly imagine and describe distressing experiences as a way to reduce the trauma's power over their psychological well-being.

Two-Factor Theory

A psychological theory proposing that human behavior is influenced by both associative and reinforcement processes.

Anxiety Reduction

Techniques or strategies aimed at decreasing feelings of anxiety, which can include behavioral, cognitive, or pharmacological methods.

Avoidance Responses

Behaviors aimed at preventing exposure to unpleasant or feared stimuli, often discussed in the context of anxiety and phobias.