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Применение производной к исследованию функций. PowerPoint PPT Presentation


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Применение производной к исследованию функций. Чугуева Любовь Николаевна. Учитель математики МБОУ СОШ №59 п. Белозёрный. С ОДЕРЖАНИЕ. Задания на соответствие. Математическое лото. Устные задания. y. 0. х. k = sin. Угловым коэффициентом прямой называется. k = tg. k = ctg.

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Применение производной к исследованию функций.

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6122562

.

. 59 . .


6122562

.

  • .

  • .

  • .


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y

0

k = sin

k = tg

k = ctg

y=kx+b

-


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k > 0

k = 0

k < 0


6122562

k.

k = 2

k = 0

k = -1

k = - 4

k = 18


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, f() 0

  • = f()

  • (0; f(0)).

  • .

f ' ()= k= tg


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f ' () > 0

f '() = 0

f ' () < 0


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0

,

0

1

0


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0

+;

  • +

  • -;

-

-


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= f(x) [a;b].

, .

y

y = f(x)

b

a

x


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= f(x)

[a;b].

= f/(x). , .

y

y = f/(x)

b

a

x


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= f(x) (- 4; 3). . [-3;0]

= f(x) ?

y = f /(x)

-4 -3 -2 -1

1 2 3 4 5


6122562

=f/(x),

(- 5; 5). =f(x) .

y

y = f /(x)

4

3

2

1

x

1 2 3 4 5 6 7

-7 -6 -5 -4 -3 -2 -1

-1

-2

-3

-4

-5


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= f(x)

(- 6; 3). . i, i = -2+5.

y

4

3

2

1

y = f /(x)

x

-7 -6 -5 -4 -3 -2 -1

1 2 3 4 5 6 7

-1

-2

-3

-4

-5


6122562

f(x),

[-5;5).

i, , f'(xi) .

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1

1 2 3 4 5 6 7

-1

-2

-3

-4

-5

-6

-7


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. , =12.

7

6

5

4

3

2

1

-7 -6 -5 -4 -3 -2 -1

1 2 3 4 5 6 7

-1

-2

-3

-4

-5

-6

-7


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,

, ?

3

4

1

2


6122562

,

= f (). = f' ().

.


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= f(x) [a;b].

. , .

y

y = f(x)

b

a

x


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=f(x) 0.

0.

4

0

4

, k>o.

tg=4 : 4 =1. , k= 1.


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=f(x)

0.

0.

6

0

3

, k<o.

tg= 6 : 3 =2. , k= -2


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=f(x),

[-4;5]. =f(x). .

1 2 3 4 5

-4 -3 -2 -1

3


6122562

1.

2.


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