#84AB1a
var('t')
a(t)=6*t+6
integrate(a(t),t)
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var('A')
v(t)=3*t^2 + 6*t + A
solve(-9==v(0),A)
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v(t)=3*t^2 + 6*t - 9
show(v(t))
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#84AB1c
integrate(3*t^2 + 6*t-9,t)
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var('B')
x(t)=t^3 + 3*t^2 - 9*t + B
solve(-27==x(0),B)
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x(t)=t^3 + 3*t^2 - 9*t - 27
show(x(t))
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#84AB1b
p1=plot(a(t),0,2,color='red')
p2=plot(v(t),0,2,color='green')
p3=plot(x(t),0,2)
(p1+p2+p3)
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