- Главная
- Разное
- Образование
- Спорт
- Естествознание
- Природоведение
- Религиоведение
- Французский язык
- Черчение
- Английский язык
- Астрономия
- Алгебра
- Биология
- География
- Геометрия
- Детские презентации
- Информатика
- История
- Литература
- Математика
- Музыка
- МХК
- Немецкий язык
- ОБЖ
- Обществознание
- Окружающий мир
- Педагогика
- Русский язык
- Технология
- Физика
- Философия
- Химия
- Шаблоны, фоны, картинки для презентаций
- Экология
- Экономика
Презентация, доклад по математике Стационарные точки функции, 10 класс
Содержание
- 1. Презентация по математике Стационарные точки функции, 10 класс
- 2. The stationary points of a curve are
- 3. The stationary points are (3, -27) and
- 4. ExercisesAns: St. pt. is ( 2, 1)Solutions:
- 5. Solution:Ans: St. pts. are ( 1, −6) and ( −2, 21 )
- 6. We need to be able to determine
- 7. So, for a max the gradients areThe
- 8. Solution:On the left of x = 2
- 9. The gradient function is given by the
- 10. Another method for determining the nature of a stationary point.The gradient function is given by
- 11. We now need to find the y-coordinates of the st. pts.
- 12. To distinguish between max and min we use the 2nd derivative, at the stationary points.
- 13. SUMMARYTo find stationary points, solve the equation
- 14. ExercisesFind the coordinates of the stationary points
The stationary points of a curve are the points where the gradient is zeroA local maximumA local minimumxxThe word local is usually omitted and the points called maximum and minimum points.e.g.
Слайд 2The stationary points of a curve are the points where the
gradient is zero
A local maximum
A local minimum
x
x
The word local is usually omitted and the points called maximum and minimum points.
e.g.
Слайд 3The stationary points are (3, -27) and ( -1, 5)
Tip: Watch
out for common factors when finding stationary points.
Слайд 6We need to be able to determine the nature of a
stationary point ( whether it is a max or a min ). There are several ways of doing this. e.g.
Слайд 7So, for a max the gradients are
The opposite is true for
a minimum
At the max
On the right of the max
On the left of the max
Calculating the gradients on the left and right of a stationary point tells us whether the point is a max or a min.
Слайд 8Solution:
On the left of x = 2 e.g. at x =
1,
On the right of x = 2 e.g. at x = 3,
We have
Substitute in (1):
Слайд 9The gradient function is given by
the gradient is 0
Another method
for determining the nature of a stationary point.
Слайд 10Another method for determining the nature of a stationary point.
The gradient
function is given by
Слайд 14Exercises
Find the coordinates of the stationary points of the following functions,
determine the nature of each and sketch the functions.
1.
2.
