Критические точки Quiz

Найдите производную функции f(x) = x^2 - 4x + 5.

• f'(x) = 2x - 4

• f'(x) = 2x + 4

• f'(x) = 3x - 4

• f'(x) = x^2 - 4

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

• The critical points are x = 1 + i√(2/3) and x = 1 - i√(2/3)

• The critical points are x = 2 + i√(2/3) and x = 2 - i√(2/3)

• The critical points are x = -1 + i√(2/3) and x = -1 - i√(2/3)

• The critical points are x = 0 + i√(2/3) and x = 0 - i√(2/3)

Проверьте точку x = 2 на экстремумы функции h(x) = x^3 - 6x^2 + 9x.

• x = 2 is a saddle point

• x = 2 is a local minimum

• x = 2 is not a point of extremum.

• x = 2 is a local maximum

Найдите производную функции f(x) = 2x^3 - 9x^2 + 12x - 5.

• f'(x) = 6x^2 - 18x + 10

• f'(x) = 6x^2 - 18x + 15

• f'(x) = 4x^3 - 9x^2 + 12x - 5

• f'(x) = 6x^2 - 18x + 12

Найдите критические точки функции g(x) = x^4 - 4x^3 + 6x^2 - 4x.

• The critical points are x = -1 and x = -1.

• The critical points are x = 1 and x = 1.

• The critical points are x = 2 and x = 2.

• The critical points are x = 0 and x = 0.

Проверьте точку x = 3 на экстремумы функции h(x) = -x^3 + 6x^2 - 9x + 4.

• The point x = 3 is not a critical point for the function h(x) = -x^3 + 6x^2 - 9x + 4.

• The point x = 3 is a local maximum for the function h(x) = -x^3 + 6x^2 - 9x + 4.

• The point x = 3 is a point of inflection for the function h(x) = -x^3 + 6x^2 - 9x + 4.

• The point x = 3 is a local minimum for the function h(x) = -x^3 + 6x^2 - 9x + 4.

Найдите производную функции f(x) = 3x^4 - 8x^3 + 6x^2 + 2x - 1.

• f'(x) = 12x^3 - 24x^2 + 12x - 2

• f'(x) = 12x^3 - 24x^2 + 12x + 1

• f'(x) = 12x^3 - 24x^2 + 12x

• f'(x) = 12x^3 - 24x^2 + 12x + 2

Найдите критические точки функции g(x) = 4x^5 - 20x^4 + 40x^3 - 40x^2 + 20x.

• The critical points of the function g(x) = 4x^5 - 20x^4 + 40x^3 - 40x^2 + 20x are x = 0, x = 1, x = 2.

• x = -1

• x = 3

• x = 4

Проверьте точку x = 1 на экстремумы функции h(x) = 2x^4 - 8x^3 + 8x^2 - 2x + 3.

• Local minimum

• Global maximum

• Saddle point

• Local maximum

Найдите производную функции f(x) = x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1.

• f'(x) = 5x^4 - 20x^3 + 30x^2 - 20x + 5

• f'(x) = 5x^4 - 20x^3 + 30x^2 - 20x + 4

• f'(x) = 5x^4 - 20x^3 + 30x^2 - 20x + 6

• f'(x) = 5x^4 - 20x^3 + 30x^2 - 20x + 3