Do not include 5 or 10, since the first derivative is zero
↓ (5,10)
Increasing interval
Particle Motion
Level 1
v(t) this is the first derivative Keep in mind that velocity is the average rate of positions
If the particle is moving, we have to use v(t)
velocity is negative and implies a left motion
t = 1 v(1) v(1) = 3(1) − 2 6(1)−9 v(1) = 3−6−9 v(1) = −12
so, equal the first derivative to zero 0 = 3t − 2 24t +45 factor the trinomial 0 = 3(t − 2 8t +15) 0 = t − 2 8t +15 5 3 t = 5 t = 3 ←these are the zeros of the first derivative ∧ particle at rest