Question

determinați valoarea minima a functiei f:R-R, f(x) =xla2 - 7x+2

Answer 1

[tex]f:\mathbb{R}\rightarrow \mathbb{R},f(x)=x^2-7x+2\\ f(x)=x^2-7x+2=x^2-7x+\dfrac{49}{4}-\dfrac{41}{4}=\left(x-\dfrac{7}{2}\right)^2-\dfrac{41}{4}\\ \text{Deoarece:}\ \left(x-\dfrac{7}{2}\right)^2\geq 0 \Rightarrow \left(x-\dfrac{7}{2}\right)^2-\dfrac{41}{4}\geq -\dfrac{41}{4}\\ \text{Deci valoarea minima este }-\dfrac{41}{4}.[/tex]