I need a help with the differential equationsquestion.

4. [10 pts.] Let f (y) be a function that satises the conditions of the Uniqueness Theorem. Let y] (t) be a solution of the autonomous differential equation 32' = f (y). Assume that y1(t) has a local minimum at D. Show that (a) f(y,.) = 0, where y* = 321(0); (1)) y1(t) = y\": for all t E (oo,oo)