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кубическая функция может иметь только локальный минимум. Потому что при х -> она уходит в
точки минимума и максимума соответствуют нулям производной
сумма степеней равна нулю, значит один корень = 1, второй = a
локальным минимумом является больший корень (кубическая функция возрастает от минус бесконечности до первого корня, потом убывает, потом снова возрастает до плюс бесконечности)
значит при a<1 локальный минимум f(x=1) = 1/3 - (a+1)/2 + a - 7 = a/2 - 7
при а>1 локальный минимум f(x=a) = a^3/3-(a+1)/2*a^2+a^2 - 7 = (1/3 - 1/2) a^3 + (-1/2+1) a^2 - 7 = - a^3 / 6 + a^2 / 2 - 7
при a = 1 имеем точку перегиба и никакого минимума
BD^{2}=\sqrt{x}255+64=\sqrt{x}289 BD=17 S=17*21=357 V=357