Question Here

[marble raft]

s=integral[3,t]f(x)dx not the one in the question

1. for 0<=t<=9, at what time does s have max value?
2. approx when is acceleration zero?
3. when's the particle moving toward the origin?
4. at t=9, on what side of the origin does the particle lie?

[feral merlin]

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[lunar silo]

For question 1, s can be treated as a function of t. And the maximum can be found using the derivative

[feral merlin]

@marble raft

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[night matrix]

For question 1, can you think of when the integral starts decreasing? The integral should decrease when taking negative values of the function f.