Final answer:
The statement that a postsynaptic potential will maintain a constant amplitude as it moves from the tip of a dendrite to the axon hillock is false because the PSP could be altered through temporal and spatial summation of various excitatory and inhibitory inputs.
Step-by-step explanation:
As it moves from the tip of a dendrite to the axon hillock, a postsynaptic potential will not maintain a constant amplitude. This statement is false. A postsynaptic potential (PSP) is a local, graded change in the membrane potential. Excitatory postsynaptic potentials (EPSPs) can depolarize the membrane, moving the potential towards the threshold, while inhibitory postsynaptic potentials (IPSPs) can hyperpolarize it, moving the potential away from the threshold.
PSPs are subject to temporal and spatial summation, where multiple signals can add together to influence whether the membrane reaches the excitation threshold necessary to fire an action potential. The summing occurs at the axon hillock. Thus, as PSPs travel towards the axon hillock, their amplitudes can change based on the various inputs the neuron is receiving, which may include EPSPs and IPSPs from numerous synapses.