Question

sub lll,1-a,b,c,va rog,urgent

Answer 1

[tex]\it f(x)=x - 3lnx [/tex]


$\it b)\ f'(x) = (x-3lnx)' = 1-\dfrac{3}{x} =\dfrac{x-3}{x}$

$\it \lim_{x\to2} \dfrac{f(x) - f(2)}{x-2} =f'(2) =\dfrac{2-3}{2}=-\dfrac{1}{2}$

$\it c) \ Ecuatia\ tangentei\ este \ : \ \ y-f(1) =f'(1)(x-1)$

$\it f(1) = 1-3ln1=1-3\cdot0=1$

$\it f'(1) = \dfrac{1-3}{1} = -2$

$\it Obtinem\ ecuatia\ tangentei\ : \ \ y-1 = -2(x-1) \Rightarrow y=-2x+3$