A)f(x)=f(x₀)+f'(x₀)(x-x₀);
f(x₀)=3x₀^2-2x₀+5=3*1²-2*1+5=3-2+5=6;
f'(x)=6x-2; f'(x₀)=6x₀-2=6*1-2=4;
f(x)=6+4(x-1)=6+4x-4=2+4x;
б)f(x₀)=4x₀³/3-4x₀=4*1/3-4=-1/3;
f'(x)=4x²-4;
f'(x₀)=4x₀²-4=4*1-4=0
f(x)=f(x₀)+f'(x₀)(x-x₀)=-1/3+0*(x-1)=-1/3;
в)y=12x^3-3x^2+x-3
f(x₀)=12*1-3*1+1-3=7
f'(x)=36x²-6x+1;
f'(x₀)=36*1-6*1+1=31;
f(x)=f(x₀)+f'(x₀)(x-x₀)=7+31(x-1)=7+31x-31=31x-24.