Question

Найдите наибольшие наименьшие значения функции на заданном интервале : x e [-3;1]; f (x) = 3x^4 -16^3 +2

Answer 1

1) f(-3) = 243 - 432 + 2 = 677

2) f(1) = 3 - 16 + 2 = -11

3) f'(x) = 12x^3 - 48x^2

4) f'(x) = 0

12x^3 - 48x^2 = 0

12x^2 (x - 4) = 0

x = 0, x = 4

{[x = 0

{[x = 4 x = 0

{ x € [-3 ; 1]

5) f(0) = 2

max f(x) = f(-3) = 677

[-3 ; 1]

min f(x) = f(1) = -11

[-3 ; 1]

Ответ : -11, 677