Question

Se considera functia f(x) = x² +x+2/x+2.
a) Ecuatia asimptotei oblice a graficului functiei catre +infinit.
b)f'(x)
c) Punctele de extrem ale functiei f.

Answer 1

f:R/{-2}->R
a) as. oblica e de forma y=mx+n, m, n finite
forme generale:
m = $\lim_{x \to \infty} \frac{f(x)}{x}$
n = $\lim_{x \to \infty} [f(x) -m*x]$
deci, m = $\lim_{x \to \infty} \frac{x^2+x+2}{x+2}* \frac{1}{x}$
<=> m = $\lim_{x \to \infty} \frac{x^2+x+2}{x^2+2x}$
avand acelasi grad => m=1.
n = $\lim_{x \to \infty} \frac{x^2+x+2-x^2-2x}{x+2}$
<=> n = $\lim_{x \to \infty} \frac{-x+2}{x+2}$ = -1
deci, y= x-1 asimptota oblica spre +inf la graficul fct.
b) f'(x)=$\frac{(x^2+x+2)'(x+2)-(x^2+x+2)(x+2)'}{(x+2)^2}$
o termin imediat de scris, stai 15 minute ca am treaba