Question: for what value rc of the parameter r does the...

For what value Rc of the parameter r does the function f(x) = -rx^2+x^4 change from having (i) a single minimum when R smaller or equals to Rc, to (ii) two minima x1 and x2, and a maximum at x=0 when R bigger then Rc? How do x1 and x2 depend on r?

 

Answer : Rc=   , x1=      ,    x2=