Экстремумы функций

Найдите максимум функции f(x) = 3x^2 - 12x + 5.

• 4

• 10

• 2

• 6

Найдите минимум функции g(x) = x^3 - 6x^2 + 9x.

• Minimum of the function g(x) = x^3 - 6x^2 + 9x is x = -2

• Minimum of the function g(x) = x^3 - 6x^2 + 9x is x = 0

• Minimum of the function g(x) = x^3 - 6x^2 + 9x is x = 1.5

• Minimum of the function g(x) = x^3 - 6x^2 + 9x is x = 3

С помощью производной определите, является ли точка x=2 локальным минимумом функции h(x) = x^4 - 8x^2 + 16.

• No, x=2 is not a critical point of the function h(x) = x^4 - 8x^2 + 16.

• Yes, x=2 is a saddle point of the function h(x) = x^4 - 8x^2 + 16.

• No, x=2 is a local maximum of the function h(x) = x^4 - 8x^2 + 16.

• Yes, x=2 is a local minimum of the function h(x) = x^4 - 8x^2 + 16.

С помощью производной определите, является ли точка x=1 локальным максимумом функции k(x) = 2x^3 - 9x^2 + 12x - 4.

• No, x=1 is a local minimum of the function k(x)

• Yes, x=1 is a point of inflection for the function k(x)

• No, x=1 is not a local maximum of the function k(x)

• Yes, x=1 is a local maximum of the function k(x)

Найдите максимум функции l(x) = 4x^3 - 12x^2 + 6x - 2.

• The maximum of the function l(x) = 4x^3 - 12x^2 + 6x - 2 is at x = 0

• The maximum of the function l(x) = 4x^3 - 12x^2 + 6x - 2 is at x = -1

• The maximum of the function l(x) = 4x^3 - 12x^2 + 6x - 2 is at x = 2

• The maximum of the function l(x) = 4x^3 - 12x^2 + 6x - 2 is at x = 1/2.

Найдите минимум функции m(x) = x^4 - 4x^3 + 6x^2 - 4x + 1.

• 2

• 3

• 5

• 1

С помощью производной определите, является ли точка x=3 локальным минимумом функции n(x) = x^3 - 9x^2 + 24x - 20.

• The point x=3 is a local minimum of the function n(x) = x^3 - 9x^2 + 24x - 20.

• The point x=3 is a saddle point of the function n(x) = x^3 - 9x^2 + 24x - 20.

• The point x=3 is a local maximum of the function n(x) = x^3 - 9x^2 + 24x - 20.

• The function n(x) = x^3 - 9x^2 + 24x - 20 has no local extrema at x=3.

С помощью производной определите, является ли точка x=0 локальным максимумом функции p(x) = 3x^4 - 16x^3 + 24x^2 - 8x + 2.

• No, x=0 is a local minimum of the function p(x)

• Yes, x=0 is a point of inflection for the function p(x)

• No, x=0 is not a local maximum of the function p(x)

• Yes, x=0 is a local maximum of the function p(x)

Найдите максимум функции q(x) = 2x^3 - 9x^2 + 12x - 4.

• The maximum value of the function q(x) = 2x^3 - 9x^2 + 12x - 4 is q(-2) = -8.

• The maximum value of the function q(x) = 2x^3 - 9x^2 + 12x - 4 is q(2) = 4.

• The maximum value of the function q(x) = 2x^3 - 9x^2 + 12x - 4 is q(4) = 8.

• The maximum value of the function q(x) = 2x^3 - 9x^2 + 12x - 4 is q(0) = -4.

Найдите минимум функции r(x) = x^4 - 4x^3 + 6x^2 - 4x + 1.

• 2

• 4

• 3

• 1