7) у = х³ -12х [-1; 3] наим. значение ?
решение
у' = 3x² -12
3x² -12 = 0
x² = 4
x = +-2
2∈[-1; 3], -2∉[-1; 3]
а) х = -1; у = (-1)³ -12*(-1) = -1 +12 = 11
б) х = 3; у = 3³ -12*3 = 27 -36 = -9
в) х = 2; у = (-2)³ -12* 2 = -8 -24 = -32
Ответ: min y = -32
8) f(x) = Cos4xCosπ/3 - Sin4xSinπ/3 = Cos(4x +π/3); х₀= π/3; f'(x₀) =?
f'(x) = -4Sin(4x +π/3)
f'(x₀) = f'(π/3) = -4Sin(4*π/3 + π/3) = -4*Sin5π/3 = -4*(-√3/2) = -2√3