Question

nu prea inteleg ce imi cere exercitiul​

Answer 1

f(x) = x²e⁻ˣ

f'(x) = 2xe⁻ˣ - x²e⁻ˣ

f'(0) = 0

f''(x) = 2e⁻ˣ - 2xe⁻ˣ - f'(x)

f''(0) = 2

f'''(x) = -2e⁻ˣ - 2e⁻ˣ + 2xe⁻ˣ - f''(x)

f'''(0) = -2-2+0-2 = -6

fⁱᵛ(x) = 2e⁻ˣ + 2e⁻ˣ + 2e⁻ˣ - 2xe⁻ˣ - f'''(x)

fⁱᵛ(0) = 2+2+2-0-(-6) = 12

fᵛ(x) = -2e⁻ˣ - 2e⁻ˣ - 2e⁻ˣ - 2e⁻ˣ + 2xe⁻ˣ - fⁱᵛ(x)

fᵛ(0) = -2-2-2-2-12 = -20

fᵛⁱ(x) = 2·4e⁻ˣ + 2e⁻ˣ - 2xe⁻ˣ - fᵛ(x)

fᵛⁱ(0) = 2·4·1 + 2·1 - 0 - (-20) = 8 + 2 + 20 = 30

⇒ n = VI ⇒ n = 6