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A function ƒ(t) is given by
ƒ(t) = at(cos(t^2)) + b
a and b are constants.
f(t) is the velocity in ft/min. of an incredibly indecisive high school boy from his lunch table at time t, moving towards his crush sitting on the other side of the cafeteria.
at t = 0 the boy gets up from his table and begins moving at a rate of 2 ft/min, accelerating towards the human of his dreams at 4 ft/min^2.
What is the distance between the seats of the two potential lovers?