# Η ΕΝΝΟΙΑ ΤΗΣ ΠΑΡΑΓΩΓΟΥ

• View
35

0

Embed Size (px)

Transcript

1. 1. . . . . . 2.1
2. 2. , A. ,
3. 3. f A(,f()). f o B (, f()) 0 f(0) f() . : .ggb
4. 4. : 0 f(0) f() h = -0 ( h0) . f 0, : 0 0 )()( lim 0 xx xfxf xx = o ( ) , f 0.
5. 5. H 0
6. 6. . ( ) t =f(t). A t=0 t=t0 t=t B h = t-t0 =u 0 0 )()( tt tftf = B t=t t0 h h 0 . 0 0 0 )()( lim)( 0 tt tftf tu tt = h ( ) , o f ( ) t t0.
7. 7. . 0 0 0 )()( lim 0 ff f 0 , f 0 f (x0) .
8. 8. h = x-x0 x = x0 +h : h = x-x0 x, f(x0 + h)- f(x0) = f(x0 + x ) - f(x0) f(x0) , : = )( lim)(' 0 0 f xf o h fhf xf h o )()( lim)(' 00 0 + =
9. 9. , x0 f, : f x0 , . 0 0 )()( lim 0 ff 0 0 )()( lim 0 + ff
10. 10. f ( f () ) ) f A(,f()) . 0 f = f () B) 0 , f(x) . u(x0) = f (x0) ) f 0 y = f (x) =0
11. 11. 1 1 f(x) = 3x2 0=1 h fhf xf h o )()( lim)(' 00 0 + = f (1) . : 0=1 h fhf f h )1()1( lim)1(' 0 + = h h h 22 0 13)1(3 lim + = h hh h 3)21(3 lim 2 0 ++ = h hh h 3633 lim 2 0 ++ = h hh h 63 lim 2 0 + = h hh h )2(3 lim 0 + = )2(3lim 0 += h h 3= 3)1(' =f f A(1,f(1)) 3
12. 12. 2 2 t s(t) = t2 +t.( sec) 2 sec h shs su h )2()2( lim)2(')2( 0 + == h hh h )22()2()2( lim 22 0 ++++ = h hhh h 62)44( lim 2 0 ++++ = h hhh h 6244 lim 2 0 ++++ = h hh h 5 lim 2 0 + = h hh h )5( lim 0 + = )5(lim 0 += h h 5= 2 sec 5 m/sec
13. 13. Cf f. A(x0 , f (x 0)) f x0. , = f(x0) : y - f (x0) = f(x0) (x - x0 ) f(x0) A( x 0 , f (x0)) Cf f x0. .
14. 14. 3 f A(0,1) /4 0 = 0 : 3.ggb
15. 15. . f ' x0, . x x0 f x0. , f x0. )()(lim 0 0 xfxf xx =
16. 16. f ' x0, , , x0. f x0 , ' .
17. 17. 4 f 0 = 0 0 . : 4.ggb
18. 18. 5 x2 x + , 2 f(x) = x 1