Calc question. Find G(t)

Question

Given G''(t)= t³ - t, G'(0)= 1, G(0)= -1. Find G(t)

Answer 1

To find g(t) you will need to start with the g"(t) equation and take the general integral of both sides.

g"(t)=t^3-t

g'(t)=t^4/4-t^2/2+c

plug in g(0)=1 and solve for c

take the general integral of g' now.

g'(t)=t^4/4-t^2/2+1

g(t)=t^5/20-t^3/6+t+c

now plug in g(0)=-1 and solve for c

that should give you you answer!