Final answer:
If an EPSP depolarizes the axon hillock by 40mV and an IPSP hyperpolarizes the axon hillock by 15mV, the neuron would still reach threshold and fire an action potential.
Step-by-step explanation:
A neuron at rest has a resting membrane potential of -70mV. If an EPSP depolarizes the axon hillock by 40mV and an IPSP hyperpolarizes the axon hillock by 15mV, the net change in voltage is 25mV (40mV - 15mV). This would bring the membrane potential to -45mV (-70mV + 25mV).
The threshold for action potential is -40mV. Since the net change in voltage (-45mV) would exceed the threshold, the neuron would fire an action potential.
Therefore, in this scenario, the EPSP and IPSP would cancel each other out, and the neuron would still reach threshold and fire an action potential.