f ' ( x ) = ( - x² + 2x ) / ( x² - x + 1 ) ²
↓
≠ 0 , cu Δ = 1 - 4 = - 3 <0
f ' ( x ) = 0 daca - x² + 2x = 0 ⇒ - x ( x - 2) = 0 ⇒ x₁ = 0
x₂ = 2
monotonia = semn pentru f '
x -∞ 0 2 +∞
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f ' - 0 + 0 - -
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f ↓ ↓ ↓
monoton descr. cres. descr.
x∈( -∞ ,0) x∈ ( 0 , 2 ) x∈(2, +∞)
