, , .
: y``x = d2y/dx2 ( ).
: = 2+2-1
I : ' = 3 * 2 + 2 * 1- 0 = 6 + 2
II : " = 6 * 1 + 0 = 6
I : υ = dS/dt
II : a = dυ = d2S/dt2
, , ( , ).
: = 6 +
y`x = dy/dx = 6x5 + ex, y``x = d2y/dx2 = 30x4 + ex, y```x = d3y/dx3 = 120x3 + ex,
xIV = d4y/dx4 = 3602+, V = d5y/dx5 =720 + , x VI = d6y/dx6 = 720 +x
.
, , , .
: = 22 + 4 + 5, ' = 4 + 4
4 + 4 > 0 .. > -1 ,
4 + 4< 0 .. < -1 .
= -1, = 2(-1)2 + 4(-1) + 5 = 3. = -1 (min).
.
.
(.. max min).
= , 0 , , f(a) > f(x).
= , 0 , , f(a) < f(x).
: = 2+1
1. ' = 2
2. y`x = 2 = 0
= 0 - .
3. ) (0) = 02 + 1 = 1
)(-1) = (-1)2+1 = 2
)(1)= 12+ 1 =2
y(0) < y (1), = 0, min.
0 = , f'() < 0, , f'(a)> , .
, f'(x) .
= f(x).
y` = lim∆x→0∆y/∆x
, ` ∆y/∆x - α.
∆y/∆x = y`x + α. ∆: ∆ = ' ∆ + α∆
α∆ α , , dy; .. dy = yx'∆x. : dx = ∆,
|
|
dy = y`xdx, y`x = dy/dx
.
CD = AC tg α1, AC = ∆x, a tgα = y`x ( ), CD = 'x dx, yx'dx = dy;
CD = dy
, , ∆.