Найдите наибольшее значение функции y=(x-2)^2*e^x на отрезке [-5; 1] найдите наименьшее значение функции y=cosx+18/п*x+7 на отрезке [-2п/3; 0]

1) найдем производную функции:  

2) найдем кретические точки:  

 

возможно ошибся

метод интервалов.

1) х² + 5х + 4 = 0

корни -1 и -4

2) х² -6х -7 = 0

корни -1 и 7

3) х² + 8х +16 = 0

    (х + 4)² = 0

корень - 4

-∞                 (-4)           [-1]             [7]               + ∞

          +                   -               +               +           это знаки х² + 5х + 4

          +                 +               -                 +           это знаки   х² -6х -7

          +                 +               +                 +           это знаки   х² + 8х +16

iiiiiiiiiiiiiiiiiiiiiii                                   iiiiiiiiiiiiiiiiiii   это решение неравенства

ответ: х ∈(-∞ ; -4)∪[7; + ∞)

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