fraszka001: D=R \ { 4/5 ; 1 }
f'(x)=0
| | (4x−5)' | | (x2 −1) − (x2 −1)' (4x−5) | |
f'(x)= |
| = |
| = |
| | x2 −1 | | (x2 −1)2 | |
| | 4x2−4−8x2+10x | | −4x2+10x−4 | |
= |
| = |
| |
| | (x2 −1)2 | | (x2 −1)2 | |
(−4x
2+10x−4)(x
2 −1)
2 =0
Δ=100−64=36 ;
√Δ=6
x1=2 ; x2=1/2 ;
f'(x)<0 ⇔ x ∊ (−
∞;1/2) ∪ (2;+
∞) ⇒ f(x) ↘
f'(x)>0 ⇔ x ∊ (1/2;2) ⇒ f(x) ↗
x min = 1/2
x/max = 2
min :
| | 4(1/2)−5 | |
f(1/2)= |
| = 4 |
| | (1/2)2 − 1 | |
max:
| | 4(2)−5 | |
f(2)= |
| = 1 |
| | (2)2 − 1 | |
...i powinno być dobrze!
jak coś to mnie poprawcie
