Найти точку минимума функции y=4 х-4ln (х+7)

y = 4x - 4ln (x + 7),

x + 7 > 0,

x > - 7,

y' = 4 - (4 / (x + 7))

y' = (4x + 28 - 4) / (x + 7) = (4x + 24) / (x + 7),

y' > 0,

y' > (4x + 24) / (x + 7) > 0 → x = ( - ∞; - 7) V (-6; ∞),

y' < 0

y' < (4x + 24) / (x + 7) < 0 → x = (-7; - 6),

x = - 6 → ymin

y (-6) = 4 * - 6 - 4ln (-6 + 7) = - 24 - 4ln1 = - 24 - 0 = - 24,

MIN (-6; -24)