f(x) = x⁴ - 8x² + 12
punctele de extrem ⇒ f' (x) = 4x³ - 8 ·2x = 4x³ - 16x = 4x ·( x² - 4 )
si f'(x) = 0
4x · ( x -2) ·( x + 2) = 0
x₁ = 0 ; x₂ = 2 ; x₃ = - 2 radacinile derivatei I
studiu de semn :
x -∞ -2 0 2 +∞
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f' --- 0 + 0 --- 0 + +
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f md mc md mc mc =monotn cres
md=monoton desc
min MAX min
⇵ ⇵ ⇵
(-2;-4) (0;12) (2; -4)
