32. Найти f′(0) и f′(2), если: 1) f(x)=x²−2x+1; 2) f(x)=x³−2x; 3) f(x)=−x³+2x²; 4) f(x)=3x²+x+1.

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

   \(f'(x)=2x-2\).

   \(f'(0)=-2\), \(f'(2)=4-2=2\).

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

   \(f'(x)=3x^2-2\).

   \(f'(0)=-2\), \(f'(2)=3\cdot 4-2=10\).

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

   \(f'(x)=-3x^2+4x\).

   \(f'(0)=0\), \(f'(2)=-3\cdot 4+4\cdot 2=-4\).

4. \(f(x)=3x^2+x+1\).

   \(f'(x)=6x+1\).

   \(f'(0)=1\), \(f'(2)=12+1=13\).

Ответ: 1) \(f'(0)=-2\), \(f'(2)=2\); 2) \(f'(0)=-2\), \(f'(2)=10\); 3) \(f'(0)=0\), \(f'(2)=-4\); 4) \(f'(0)=1\), \(f'(2)=13\).