Let f(y) be a continuous function:

Suppose that f(-10)>0 and f(10)<0, show that there is a equilibrium point for dy/dt=f(y) between y=-10 and y=10.

Just realized I posted this is in the wrong section, should be in Differential Equations, sorry.

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- January 26th 2010, 11:08 AMLenEquilibrium point
Let f(y) be a continuous function:

Suppose that f(-10)>0 and f(10)<0, show that there is a equilibrium point for dy/dt=f(y) between y=-10 and y=10.

Just realized I posted this is in the wrong section, should be in Differential Equations, sorry. - January 26th 2010, 01:07 PMCalculus26
Recall an equillibrium solution occurs where f(y) = 0 for dy/dt = f(y)

By the Intermediate Value Theorem if f(10) < 0 and f(-10) > 0

Then f has a zero between -10 and 10 - January 28th 2010, 09:54 AMLen
Thanks, I didn't even think to apply that.

The**intermediate value theorem**states the following: If the function*y*=*f*(*x*) is continuous on the interval [*a*,*b*], and*u*is a number between*f*(*a*) and*f*(*b*), then there is a*c*∈ [*a*,*b*] such that*f*(*c*) =*u*.

For anyone else who reads.