| f(x+h)−f(x) | ||
musisz policzyć granicę z | przy h→0, a potem za x podstawić x0 | |
| h |
| 5(x+h)−4−[5x−4] | 5x+5h−4−5x+4 | 5h | |||
= | = | =5 [więc granica to 5] | |||
| h | h | h |
| 5(1+h)−4−(5*1−4) | ||
limh→0 | ||
| h |
| 5+5h−4−5+4 | ||
limh→0 | ||
| h |
| 5h | ||
limh→0 | ||
| h |
| f(x)−f(1) | 5x−4−5*1+4 | |||
f'(1) = limx→1 | = limx→1 | = | ||
| x−1 | x−1 |
| 5(x−1) | ||
limx→1 | = limx→1 5 = 5 | |
| x−1 |