Question

Verificati daca functia f:R->R , f(x)=x^3+x+1 este injectiva

Answer 1

$Calculam\ derivata\\ \frac{df(x)}{dx}=3x^2+1 \\ \Delta=0-4\cdot3\cdot1=-12\ \textless \ 0 \\ Nu\ avem\ puncte\ critice;\ derivata\ e\ strict\ pozitiva\Rightarrow \\ functia\ f\ este\ strict\ crescatoare. \\ Fiind\ strict\ crescatoare\Rightarrow e\ injectiva.$