1) Уравнение касательной в общем виде:
y = f(xo) + f '(xo)(x - xo)
f(2) = 2² - 6*2 + 5 = 4 - 12 + 5 = - 3
f '(x) = (x² - 6x + 5) ' = 2x - 6
f '(2) = 2*2 - 6 = 4 - 6 =- 2
y =- 3 - 2(x - 2) = - 3 - 2x + 4 = - 2x + 1
Уравнение касательной y = - 2x + 1
2) f(e) = lne = 1
f '(x) = (lnx) ' = 1/x
f '(e) = 1/e
y = 1 + 1/e(x - e) = 1 + 1/eX - 1 = 1/eX
3) f(1) = 3¹ = 3
f '(x) = (3ˣ) ' = 3ˣ * ln3
f '( 1) = 3¹ * ln3 = 3ln3 = ln27
y = 3 + ln27(x - 1) = 3 + ln27X - ln27 = ln27X + 3 - ln27