Question

Fie m un numar real arbitrar fixat. Notam cu M maximul functiei f : R -> R
f(x)= -x²+mx-1-m². Care din urmatoarele afirmatii este adevarata?
a)M=1
b)M>-1
c)M∈∅
d)M≤-1
e)M=0
f)M=$\frac{1}{2}$

Answer 1

[tex]M= -\dfrac{\Delta}{4a} = - \dfrac{\ \Delta}{-4} =\dfrac{\Delta}{4}\ \ \ \ (1) [/tex]

[tex]Calculam\ \Delta\ si\ obtinem: \\\;\\ \Delta = -4-3m^2\ \ \ \ (2)[/tex]

$(1), (2) \Longrightarrow M = \dfrac{-4-3m^2}{4} =\dfrac{-4}{4} -\dfrac{3m^2}{4} =-1-\dfrac{3m^2}{4} \leq -1$