, x = j(t) t = ().
= y(t) y = y[()].
.. () ,
:
, , .
.
1: ,
2: : .
x2 = a2cos2t;
: .
1. (-¥; ¥).
2. .
3. : c : x = 0; y = 1;
: y = 0; x = 1;
4. : .
: y = kx + b;
: = - .
5. , .
. , ¢< 0 ¹ 0, , . = 0 , , , = 0 . , .
y¢¢ = 0 =0 y¢¢ = ¥ = 1.
(0,1) (1,0) , .. y¢¢(1-h) < 0; y¢¢(1+h) >0; y¢¢(-h) > 0; y¢¢(h) < 0 h > 0.
6. .
: .
1. , = 0.
2. .
3. : c : y = 0; x =
: x = 0; y .
4. = 0 , , = 0 .
: y = kx + b.
= .
5. .
; y¢ = 0 = 2, ¢ = ¥ = 0.
y¢ > 0 Î (-¥, 0) ,
y¢ < 0 Î (0, 2) ,
¢ > 0 Î (2, ¥) .
, (2, 3) .
/ .
> 0 ¹ 0, , , .
6. .
: .
|
|
1. Î (-¥, ¥).
2. .
3. : : x = 0, y = 0;
: y = 0, x = 0, x = 1.
4. .
.
y = kx + b.
- .
5. .
43 92 +6 1 = 0.
.
,
= 1. :
4x3 9x2 + 6x 1 x - 1
` 4x3 4x2 4x2 5x + 1
- 5x2 + 6x
` - 5x2 + 5x
x - 1
` x - 1
( 1)(42 5 + 1) = 0. : x = 1 x = ¼.
. , :
: 12x2 18x + 6. , :
x = 1, x = ½.
:
(-¥; ¼) | 1/4 | (¼; ½) | 1/2 | (½; 1) | (1; ¥) | ||
f¢¢(x) | + | + | + | - | + | ||
f¢(x) | - | + | + | + | + | ||
f(x) | . | min | . | . | . |
6. .