Найдите точку максимума функции y = (x-5) ^2*e^-2-x

Y' = ((x-5) ²*e⁻²⁻ˣ) '=0

(2 * (x-5)) * e⁻²⁻ˣ + (x-5) ² * (-e⁻²⁻ˣ) = 0

e⁻²⁻ˣ * (2x-10 - (x²-10x+25)) = 0

e⁻²⁻ˣ * (2x-10-x²+10x-25) = 0

e⁻²⁻ˣ * (-x²+12x-35) = 0

-e⁻²⁻ˣ * (x²-12x+35) = 0

e⁻²⁻ˣ * (x²-12x+35) = 0

e⁻²⁻ˣ>0 ⇒

x²-12x+35=0 D=4

x₁=5 x₂=7

y (5) = (5-5) ²*e^ (-2-5) = 0²*e⁻⁷=0

y (7) = (7-5) ²*e⁻⁷=2²*e⁻⁹=4/e⁹=ymax