assuming that g is continuous on [a,b] and that g(t) is greater than or equal 0 for all t in [a,b]

suppose that there is some y in [a,b] such g(y)>0. since g is cont on [a,b], a subinterval [c,d] containing y can be found for which g(t) > 1/2 (g(y)) where c<t<d.

may i know how g(t) > 1/2 (g(y)) is obtained?

thanks