Функция f(x) = (x - 2)/(x -3)²
Производная f'(x) = (1 ·(x -3)² - (x - 2) · 2(x - 3))/(x - 3)⁴ =
= (x - 3)((x - 3) - 2(x - 2))/(x - 3)⁴ = (x - 3 - 2x + 4)/(x - 3)³ =
= (1 - x)/(x - 3)³
Уравнение касательной к графику функции имеет вид
у = f(xo) + f'(xo) · (x - xo)
xo = 1.6
f(xo) = (1.6 - 2)/(1.6 - 3)² = -0.4/1.96 = -10/49
f'(xo) = (1 - 1.6)/(1.6 - 3)³ = -0.6/(-2.744) = 75/343
y = -10/49 + 75/343 · (x - 1.6)
y = -10/49 + 75x/343 - 75/343 · 1.6
y = 75x/343 - 10/49 - 120/343
y = 75x/343 - 70/343 - 120/343
y = (75x - 190)/343