The Function Has a Non-Removable Discontinuity at X = 0

question 348

Essay

The function has a non-removable discontinuity at x = 0. The mean value theorem does not apply.
-Let f have a derivative on an interval I. f' has successive distinct zeros at x = 1 and x = 5. Prove that there can be at most one zero of f on the interval (1, 5).

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Definitions:

Resting Potential

The electrical potential of a neuron when not stimulated or involved in passage of an impulse, typically around -70mV.

Axon

a part of a neuron that conducts impulses away from the cell body towards other neurons or muscles.

Electrical Charge

A fundamental property of matter that exists in either a positive or negative state and causes it to experience a force when placed in an electromagnetic field.

All-Or-None Law

A principle that states that the strength of a response of a nerve cell or muscle fiber is not dependent on the strength of the stimulus; if a stimulus is above a certain threshold, a nerve or muscle fiber will fire.