Question

Fie functiile fm : R→R,f(x)=x^2-(m-1)x+m,
unde m∈R.
Determinati nr reale m astfel incat
Im fm ⊂ [ 1 , +∞ ).

Answer 1

functia de gradul al 2-lea are punct de minim deoarece a =1 >0 
Deci valoarea minima este - delta/4a
-delta/4a=1 
-delta/4=1 => delta este=-4
delta este 
[tex](m-1)^{2} -4m= m^{2} -2m +1 -4m= [/tex]
[tex] m^{2} -6m +1= m^{2}-6m+1=-4 [/tex][tex] m^{2}-6m+5=0 [/tex]
calculam delta2
[tex]delta2= 36-20=16 [/tex]
$m1 = \frac{-b - \sqrt{delta2} }{2} =\ \textgreater \ M1= \frac{2}{2} =\ \textgreater \ M1=1$