Question

f:(2, infinit) cu valori R, f(x)= x-1/x-2.
Det. ecuatia tangentei la graficul functiei f in punctul x=3, situat pe graficul functiei f>
Multumesc!

Answer 1

[tex]f(x)= \frac{x-1}{x-2} [/tex]

[tex]y-y_{0}=m(x-x_{0} ) y_{0}=f(x_{o}) mt=f`(x_{0} ) x_{0} =3 [/tex]

$y-f(x_{0})=f`(x_{0} ) (x- x_{0})$

$f`(x)= (\frac{x-1}{x-2} )`= \frac{(x-1)`(x-2)-(x-1)(x-2)`}{(x-2)^2} = \frac{x-2-x+1}{(x-2)^2}= \frac{-1}{(x-2)^2}$

$f(3)= \frac{3-1}{3-2}= \frac{2}{1}=2$

$f`(3)= \frac{-1}{(x-2)^2}= \frac{-1}{(3-2)^2} = \frac{-1}{1}=-1$

[tex]y-2=-1(x-3) y-2=-x+3 y-2+x-3=0 x+y-5=0 y=-x+5[/tex]