20 uždavinys
Sprendimas.
( x^3+
- 6* x-2)′ =
0
| 3* x^2 |
| / 2 |
0
|
( x^3+
- 6* x-2)′ = 0$$(x^{3}+\frac{3\cdot x^{2}}{2}-6\cdot x-2)'$$ = $$0$$
| 3* x^2 |
| / 2 |
$${\normalsize (x^{3}+\frac{3\cdot x^{2}}{2}-6\cdot x-2)'}$$ = $${\normalsize (x^{3})'+(\frac{3\cdot x^{2}}{2})'-(6\cdot x)'-2'}$$
Paaiškinimas:
Paaiškinimas: Sumos išvestinė (f+g)′ = f′ + g′
( x^3)′+ (
)′- ( 6* x)′- 2′ = 0$$(x^{3})'+(\frac{3\cdot x^{2}}{2})'-(6\cdot x)'-2'$$ = $$0$$
| 3* x^2 |
| / 2 |
$${\normalsize (x^{3})'}$$ = $${\normalsize 3\cdot x^{2}}$$ Paaiškinimas:
Paaiškinimas: Laipsnio išvestinė, kur n = 3
3* x^2+ (
)′- ( 6* x)′- 2′ = 0$$3\cdot x^{2}+(\frac{3\cdot x^{2}}{2})'-(6\cdot x)'-2'$$ = $$0$$
| 3* x^2 |
| / 2 |
$${\normalsize (\frac{3\cdot x^{2}}{2})'}$$ = $${\normalsize 3\cdot x}$$ Paaiškinimas:
Paaiškinimas: Laipsnio išvestinė, kur n = 2
3* x^2+ 3* x- ( 6* x)′- 2′ = 0$$3\cdot x^{2}+3\cdot x-(6\cdot x)'-2'$$ = $$0$$
$${\normalsize (6\cdot x)'}$$ = $${\normalsize 6}$$ Paaiškinimas:
Paaiškinimas: x išvestinė yra 1
3* x^2+ 3* x-6- 2′ = 0$$3\cdot x^{2}+3\cdot x-6-2'$$ = $$0$$
$${\normalsize 2'}$$ = $$0$$ Paaiškinimas:
Paaiškinimas: Konstantos išvestinė yra 0
3* x^2+ 3* x-6-0 = 0$$3\cdot x^{2}+3\cdot x-6-0$$ = $$0$$
3* x^2+ 3* x-6 = 0$$3\cdot x^{2}+3\cdot x-6$$ = $$0$$
$${\normalsize 3\cdot x^{2}+3\cdot x-6}$$ = $${\normalsize 3\cdot (x^{2}+x-2)}$$ Paaiškinimas:
Paaiškinimas: 3 iškeltas prieš skliaustus
3* ( x^2+x-2) = 0$$3\cdot (x^{2}+x-2)$$ = $$0$$
$${\normalsize x^{2}+x-2}$$ = $${\normalsize (x-1)\cdot (x+2)}$$ Paaiškinimas:
Paaiškinimas: Kvadratinis trinaris $${\normalsize a\cdot x^{2}+b\cdot x+c}$$, kur
a = 1, b = 1, c = -2.
Diskriminantas $${\normalsize D = b^{2}-4\cdot a\cdot c = 1-(-8)}$$ = 9.
x1 = $${\normalsize \frac{-1+\sqrt {9}}{2\cdot 1} = \frac{-1+3}{2} = \frac{2}{2}}$$ = 1
x2 = $${\normalsize \frac{-1-\sqrt {9}}{2\cdot 1} = \frac{-1-3}{2} = \frac{-4}{2}}$$ = -2
a = 1, b = 1, c = -2.
Diskriminantas $${\normalsize D = b^{2}-4\cdot a\cdot c = 1-(-8)}$$ = 9.
x1 = $${\normalsize \frac{-1+\sqrt {9}}{2\cdot 1} = \frac{-1+3}{2} = \frac{2}{2}}$$ = 1
x2 = $${\normalsize \frac{-1-\sqrt {9}}{2\cdot 1} = \frac{-1-3}{2} = \frac{-4}{2}}$$ = -2
3* ( (x-1)* (x+2)) = 0$$3\cdot ((x-1)\cdot (x+2))$$ = $$0$$
$${\normalsize 3\cdot ((x-1)\cdot (x+2))}$$ = $${\normalsize 3\cdot (x-1)\cdot (x+2)}$$
3* (x-1)* (x+2) = 0$$3\cdot (x-1)\cdot (x+2)$$ = $$0$$
x = 1 ir x = -2
Suma 1 - 2 = -1
Atsakymas: -1