f(x) = x^4 - 8x^2 - 9 на [0, 3]экстремумы на концахf(0) = 0 - 0 - 9 = -9f(3) = 3^4 - 8*3^2 - 9 = 81 - 72 - 9 = 0или f'(x) = 0f'(x) = 4x^3 - 16x = 0x^3 - 4x = 0x(x - 2)(x + 2) = 0x = 2f(1) = 2^4 - 8*2^2 - 9 = 16 - 32 - 9 = -25-2 ∉ [0, 3]min f(2) = -25max f(3) = 0
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f(x) = x^4 - 8x^2 - 9 на [0, 3]
экстремумы на концах
f(0) = 0 - 0 - 9 = -9
f(3) = 3^4 - 8*3^2 - 9 = 81 - 72 - 9 = 0
или f'(x) = 0
f'(x) = 4x^3 - 16x = 0
x^3 - 4x = 0
x(x - 2)(x + 2) = 0
x = 2
f(1) = 2^4 - 8*2^2 - 9 = 16 - 32 - 9 = -25
-2 ∉ [0, 3]
min f(2) = -25
max f(3) = 0