1.(i)
f(x)=x², (3,9)
f'(x)=slope
2x=m (slope)
m=6 at (3,9)
y=mx+c
y=6x+c
9=6(3)+c
c=-9
y=6x-9
1.(ii)
f(x)=x³, (-2,8)
f'(x)=slope
3x²=m (slope)
m=12 at (-2,8)
y=mx+c
y=12x+c
8=12(-2)+c
c=32
y=12x+32
2.
s(t)2t^4-t²
s'(t)=v(t)=8t³-4t
v(2)=8m/s
particles moves left when v(t)<0
{t eR: 8t³-4t<0}
={t: 2t²-1<0}
={t: t²<1}
={t: t<1/sqrt2}

so, particle moves right in(1/sqrt2, infintity)