Question

решить уравнение f'(x)=0 если f(x)=(x^2-3)/(x+2)

Answer 1

$f'(x)= frac{x^2-3}{x+2}= frac{(x^2-3)'(x+2)-(x^2-3)(x+2)'}{(x+2)^2} \ f'(x)= frac{2x(x+2)-(x^2-3)*1}{(x+2)^2} \ f'(x)= frac{2x^2+4x-x^2+3}{(x+2)^2} \ f'(x)= frac{x^2+4x+3}{(x+2)^2}=0 \ x neq -2 \ x^2+4x+3=0 \ D=16-3*4=4 \ sqrt{D}=2 \ x= frac{-4+2}{2}=-1 \ x= frac{-4-2}{2}=-3$