Question

Определите точки максимума функции
F(x)=3+8x^2-x^4

Answer 1

F(x) = 3 + 8x² - x⁴

f(x) = 18x - 4x³

f(x)' = 18 - 12x²

{ 18x - 4x³ = 0

{ 18 - 12x² < 0

x(18-4x²) = 0

[ x = 0

[ 18 - 4x² = 0

[ x = 0

[ x² = 9/2

[ x = 0

[ x = +-3√2/2

18 - 12x² < 0

3 - 2x² < 0

x² < 3/2

9/2 > 3/2 => х ≠ +-3√2/2 => х = 0 => F(x) = 3 + 0 - 0 = 3

Ответ: (0; 3).