Final answer:
Failed action potentials occur when combined synapse inputs on dendrites and neuronal bodies do not depolarize the neuron enough; PSPs must reach the threshold for an action potential to be initiated. Action potentials occur at the Nodes of Ranvier due to a high density of voltage-gated Na+ channels.
Step-by-step explanation:
Failed initiations of an action potential typically occur on dendrites and neuronal bodies when the combined input of presynaptic neurons does not sufficiently depolarize the neuron. This is often due to either weak excitatory postsynaptic potentials (EPSPs) or the presence of inhibitory postsynaptic potentials (IPSPs) which move the membrane potential away from the threshold. For an action potential to be triggered, postsynaptic potentials (PSPs) must summate to reach the threshold at the axon hillock. If this threshold is reached, voltage-gated Na+ channels open, leading to rapid depolarization and the initiation of an action potential.
The resting potential is a stable, negative charge maintained inside a neuron when it is not transmitting a signal, while an action potential is a rapid, temporary change in this potential that occurs when the neuron transmits a signal. Action potentials typically occur along myelinated axons at the Nodes of Ranvier, where the concentration of voltage-gated Na+ channels is high. This strategic presence of channels within these nodes ensures efficient signal propagation along the axon.