Question

va rog dau cate puncte vreti va rog urgentt!!!!​

Answer 1

Răspuns:

a) x=1/2

b) aasa este ASA MI-A DAT SI MIE!!!

Explicație pas cu pas:

derivezi direct, nu  e asa greu??la a) apoi ecuatia o rezol;vi cu materia de clasa 7-a si a 8-a

f'(x) =1/x -2x-1= (-2x²-x+1)/x

f'(x) =0

2x²+x-1=0

x1,2=(-1±√(1+8))/4

x1=-1∉(0;∞) nu convine aici era CAPCANA

x2=1/2∈(0;∞)  convine

b) e chiar mai usor

f"(x) =(1/x -2x-1)'=-1/x²-2<0, ∀x∈R+

Answer 2

$\it a)\ x > 0\ (condi\c{\it t}ia\ de\ existen\c{\it t}\breve a\ a\ func\c{\it t}iei)\ \ \ \ (*)\\ \\ f'(x)=\dfrac{1}{x}-2x-1\\ \\ \\ f'(x)=0 \Rightarrow \dfrac{1}{x}-2x-1=0 \Big|_{\cdot x} \Rightarrow 1-2x^2-x=0 \Rightarrow \\ \\ \Rightarrow 2x^2+x-1=0 \Rightarrow 2x^2+2x-x-1=0 \Rightarrow 2x(x+1)-(x+1)=0 \Rightarrow \\ \\ \Rightarrow (x+1)(2x-1)=0 \stackrel{(*)}{\Longrightarrow}x=\dfrac{1}{2}$

$\it b)\ f''(x)=(\dfrac{1}{x}-2x-1)'=-\dfrac{1}{x^2}-2 < 0,\ \ \forall\ x\in(0,\ \infty)$