1. ## intervals

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

2. Originally Posted by alexandrabel90
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

Use limits: continuity $\Longrightarrow g(x)\xrightarrow [x\to y]{}g(y)\Longrightarrow \exists \delta > 0 \,\,s.t.\,\, |x-y|<\delta \Longrightarrow |f(y)-f(x)|<\frac{1}{2}f(y)$

(here, $\epsilon=\frac{1}{2}f(y)$ ), thus...

Tonio