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Консультация № 173501
21.10.2009, 12:25
0.00 руб.
0
3
1
Определить координаты точки графика f(x)=[$8730$]3x2+4x+3, расстояние от которой до т. B(-2;0) наименьшее
Обсуждение
21.10.2009, 13:19
общий
это ответ
Здравствуйте, Litta.
Расстояние между искомой точкой А(x; f(x)) и B(x0;f0) = В(-2;0) вычисляем по формуле
[$8730$]((х - х0)2 + (f(х) - f0)2) =
= [$8730$]((x - (-2))2 + ([$8730$](3x2 + 4x + 3) - 0)2) =
= [$8730$]((x +2)2 + 3x2 + 4x + 3) =
= [$8730$](4x2 + 8x + 7)
Найдем экстремумы функции [$966$](x) = [$8730$](4x2 + 8x + 7)
[$966$]'(x) = 4(x+1)/[$8730$](4x2 + 8x + 7)
[$966$]'(x) = 0 [$8658$] x = -1
[$966$]'(x) < 0 при х < -1, [$966$]'(x) > 0 при х > -1, значит х = -1 - точка минимума
f(-1) = √(3(-1)2+4(-1)+3) = √2
Т.о., искомая точка (-1; √2)
Расстояние между искомой точкой А(x; f(x)) и B(x0;f0) = В(-2;0) вычисляем по формуле
[$8730$]((х - х0)2 + (f(х) - f0)2) =
= [$8730$]((x - (-2))2 + ([$8730$](3x2 + 4x + 3) - 0)2) =
= [$8730$]((x +2)2 + 3x2 + 4x + 3) =
= [$8730$](4x2 + 8x + 7)
Найдем экстремумы функции [$966$](x) = [$8730$](4x2 + 8x + 7)
[$966$]'(x) = 4(x+1)/[$8730$](4x2 + 8x + 7)
[$966$]'(x) = 0 [$8658$] x = -1
[$966$]'(x) < 0 при х < -1, [$966$]'(x) > 0 при х > -1, значит х = -1 - точка минимума
f(-1) = √(3(-1)2+4(-1)+3) = √2
Т.о., искомая точка (-1; √2)
5
Огромное спасибо<br>Стало понятно, как выполнять другие задачи подобного типа
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
21.10.2009, 13:21
общий
Для наглядности можно посмотреть здесь график функции
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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