Упр.806 ГДЗ Алимов 10-11 класс (Алгебра)

1) f (х) = х2 — 2х + 1;
2) f (х)= х3 — 2х;
3) f (х) = -х3 + х2;
4) f (х) = х2 + х + 1.

1. $$f(x)=x^2-2x+1$$

   Найдём производную:

   $$f'(x)=(x^2-2x+1)’=2x-2$$

   Тогда

   $$f'(0)=2\cdot 0-2=-2$$

   $$f'(2)=2\cdot 2-2=2$$

2. $$f(x)=x^3-2x$$

   $$f'(x)=(x^3-2x)’=3x^2-2$$

   $$f'(0)=3\cdot 0^2-2=-2$$

   $$f'(2)=3\cdot 2^2-2=12-2=10$$

3. $$f(x)=-x^3+x^2$$

   $$f'(x)=(-x^3+x^2)’=-3x^2+2x$$

   $$f'(0)=-3\cdot 0^2+2\cdot 0=0$$

   $$f'(2)=-3\cdot 2^2+2\cdot 2=-12+4=-8$$

4. $$f(x)=x^2+x+1$$

   $$f'(x)=(x^2+x+1)’=2x+1$$

   $$f'(0)=2\cdot 0+1=1$$

   $$f'(2)=2\cdot 2+1=5$$

Ответ

1) $$f'(0)=-2,\ f'(2)=2$$

2) $$f'(0)=-2,\ f'(2)=10$$

3) $$f'(0)=0,\ f'(2)=-8$$

4) $$f'(0)=1,\ f'(2)=5$$