1. The correct answer is "a) makes"
Explanation: The sentence is in the present tense, so we need to use the base form of the verb. The verb "makes" is the correct form for the pronoun "she".
2. The correct answer is "a) drive, am walking"
Explanation: The sentence is talking about a habitual action in the present and an action happening at the moment. When we talk about habitual actions, we use the simple present tense, so "drive" is the correct form for the pronoun "I". For the action happening at the moment, we use the present continuous tense, so "am walking" is the correct form for the pronoun "I".
3. The correct answer is "d) does your father do"
Explanation: This question is about someone's father's profession. To ask about someone's profession, we use the auxiliary verb "do" before the subject. Therefore, "does your father do" is the correct form.
4. The correct answer is "a) is she speaking"
Explanation: The question is asking about someone's current action. To talk about an action happening at the moment, we use the present continuous tense. Therefore, "is she speaking" is the correct form for the pronoun "she".
5. The correct answer is "d) don't go"
Explanation: The sentence is in the present tense and is stating that the person does not go to the cinema very often. When we talk about present habits or routines, we use the simple present tense. Therefore, "don't go" is the correct form for the pronoun "we".
6. The correct answer is "c) are you sitting"
Explanation: The question is asking about the person's current action. To ask about an action happening at the moment, we use the present continuous tense. Therefore, "are you sitting" is the correct form for the pronoun "you".
Добрый день, я рад принять роль школьного учителя и помочь вам исследовать свойства функции Y = -x^3 + 12x^2 - 45x + 48 и построить ее график.
1. Исследование свойств функции:
a) Начнем с определения области определения функции. В данном случае, функция определена для любого значения х.
b) Далее, найдем производные функции для определения ее экстремумов и точек перегиба:
Y' = -3x^2 + 24x - 45 - первая производная
Y'' = -6x + 24 - вторая производная
c) Чтобы найти точки экстремума, решим уравнение Y' = 0:
-3x^2 + 24x - 45 = 0
Решив это квадратное уравнение, получим два значения х: х1 ≈ 2.54 и х2 ≈ 5.46.
d) Подставим найденные значения х во вторую производную, чтобы определить тип экстремума:
Y''(х1) = -6х1 + 24 ≈ 8.24 (точка минимума)
Y''(х2) = -6х2 + 24 ≈ 10.34 (точка максимума)
f) Теперь определим поведение функции в бесконечности. Рассмотрим пределы функции при x, стремящемся к плюс или минус бесконечности:
lim(x→∞) -x^3 + 12x^2 - 45x + 48 = -∞ (минус бесконечность)
lim(x→-∞) -x^3 + 12x^2 - 45x + 48 = -∞ (минус бесконечность)
g) Наконец, определим поведение функции на интервалах между найденными точками:
Y < 0 между точками минимума и максимума (2.54 < x < 5.46)
Y > 0 вне интервала (x < 2.54 или x > 5.46)
2. Построение графика функции:
a) Для построения графика используем координатную плоскость. Ось х будет горизонтальной осью, а ось Y - вертикальной осью.
b) Сначала построим основные точки, которые мы нашли в исследовании свойств функции:
- точка минимума (2.54, Y(2.54))
- точка максимума (5.46, Y(5.46))
- точка перегиба (4, Y(4))
c) Затем нарисуем график между точками минимума и перегиба и между точками перегиба и максимума. Обратите внимание, что график будет подниматься при движении от точки минимума до точки перегиба, а затем снижаться от точки перегиба до точки максимума.
d) Наконец, проведем график за пределами найденных точек, основываясь на поведении функции на этих интервалах. В данном случае, график будет отрицательным до точки минимума и после точки максимума.
В результате, мы получим график функции Y = -x^3 + 12x^2 - 45x + 48, который будет выглядеть примерно таким:
(График функции)
Надеюсь, что это решение помогло вам лучше понять исследование свойств функции и построение ее графика. Если у вас возникнут дополнительные вопросы, не стесняйтесь спрашивать.
Explanation: The sentence is in the present tense, so we need to use the base form of the verb. The verb "makes" is the correct form for the pronoun "she".
2. The correct answer is "a) drive, am walking"
Explanation: The sentence is talking about a habitual action in the present and an action happening at the moment. When we talk about habitual actions, we use the simple present tense, so "drive" is the correct form for the pronoun "I". For the action happening at the moment, we use the present continuous tense, so "am walking" is the correct form for the pronoun "I".
3. The correct answer is "d) does your father do"
Explanation: This question is about someone's father's profession. To ask about someone's profession, we use the auxiliary verb "do" before the subject. Therefore, "does your father do" is the correct form.
4. The correct answer is "a) is she speaking"
Explanation: The question is asking about someone's current action. To talk about an action happening at the moment, we use the present continuous tense. Therefore, "is she speaking" is the correct form for the pronoun "she".
5. The correct answer is "d) don't go"
Explanation: The sentence is in the present tense and is stating that the person does not go to the cinema very often. When we talk about present habits or routines, we use the simple present tense. Therefore, "don't go" is the correct form for the pronoun "we".
6. The correct answer is "c) are you sitting"
Explanation: The question is asking about the person's current action. To ask about an action happening at the moment, we use the present continuous tense. Therefore, "are you sitting" is the correct form for the pronoun "you".