Question

The Fitzhugh-Nagumo model for the electrical impulse in a neuron states that, in the absence of relaxation effects, the electrical potential in a neuron v(t) obeys the differential equation

dv/dt = −v[v² − (1 + a)v + a]

where a is a positive constant such that 0 < a < 1.

(a) For what values of v is v unchanging (that is, dv/dt = 0)?  (Enter your answers as a comma-separated list.)
v = ______

(b) For what values of v is v increasing? (Enter your answer using interval notation.)

______

(c) For what values of v is v decreasing? (Enter your answer using interval notation.)

______

Please show all work neatly, line by line, and justify steps so I can learn.

Thank you!

Answer 1

Graph of f(x) = x(x-a)(x-1), taking a = 0.4, Hope it gives an idea of what is happening to the sign of f(x)