2. f'=4-6x
f'(x₀)= f'(4)=4-6*4=-20
f(x₀)= f(4)=4*4-3*16=-32
y=f(x₀)+f'(x₀)*(x-x₀)
y=-32-20*(x-4)
y=-20x+80-32
y=-20x+48
3. (u/v)'=(u'v-uv')/v²
y'=(2*(x-2)-1*(2x-1))/(x-2)²=(2x-4-2х+1)/(x-2)²=-3/(x-2)²;
y'(-1)=-3/(-1-2)²=-3/9=-1/3
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Answers & Comments
2. f'=4-6x
f'(x₀)= f'(4)=4-6*4=-20
f(x₀)= f(4)=4*4-3*16=-32
y=f(x₀)+f'(x₀)*(x-x₀)
y=-32-20*(x-4)
y=-20x+80-32
y=-20x+48
3. (u/v)'=(u'v-uv')/v²
y'=(2*(x-2)-1*(2x-1))/(x-2)²=(2x-4-2х+1)/(x-2)²=-3/(x-2)²;
y'(-1)=-3/(-1-2)²=-3/9=-1/3