Критические точки функции

Найдите производную функции f(x) = x^2 - 4x + 4.

• f'(x) = 2x + 4

• f'(x) = 2x - 4

• f'(x) = x^2 - 4

• f'(x) = 4x - 2

Найдите нули производной функции f'(x) = 2x - 4.

• x = 4

• x = -2

• x = 2

• x = 0

Проверьте знаки производной функции f'(x) = 2x - 4 на интервалах (-∞, 2) и (2, +∞).

• The sign of the derivative on the interval (-∞, 2) is positive, and on the interval (2, +∞) is also positive.

• The sign of the derivative on the interval (-∞, 2) is positive, and on the interval (2, +∞) is negative.

• The sign of the derivative on the interval (-∞, 2) is negative, and on the interval (2, +∞) is also negative.

• The sign of the derivative on the interval (-∞, 2) is negative, and on the interval (2, +∞) is positive.

Найдите вторую производную функции f''(x) = 2.

• 3x^2 + C

• x^2 + C

• (1/3)x^3 + Cx + D

• 2x + C

Исследуйте точку x = 2 на экстремумы функции f(x) = x^2 - 4x + 4.

• The point x = 2 is a minimum point.

• The point x = 2 is a critical point.

• The point x = 2 is a maximum point.

• The point x = 2 is not a critical point.

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

• 3x^2 - 9x + 6

• 9x^2 - 18x + 6

• 9x^2 - 18x - 6

• 6x^3 - 9x^2 + 3x

Найдите нули производной функции g'(x) = 9x^2 - 18x + 6.

• x = 1 + sqrt(4)/3

• x = 1 + sqrt(2)/3

• x = 1 + sqrt(3)/3, x = 1 - sqrt(3)/3

• x = 1 - sqrt(2)/3

Проверьте знаки производной функции g'(x) = 9x^2 - 18x + 6 на интервалах (-∞, 1) и (1, +∞).

• Positive

• Negative

• Zero

• Increasing

Найдите вторую производную функции g''(x) = 18x - 18.

• g''(x) = 18x + 18

• g''(x) = 18

• g''(x) = 9x - 9

• g''(x) = 0

Исследуйте точку x = 1 на экстремумы функции g(x) = 3x^3 - 9x^2 + 6x.

• Further analysis is needed to determine the nature of the extremum at x = 1.

• The extremum is at x = 0.

• The extremum is at x = 2.

• The extremum is at x = -1.