More Applications of Derivatives 187What is the minimum and maximum acceleration of the particle on 0≤t≤7?
v(t)=
t^3
3
− 4 t^2 + 16 t− 64a(t)=v′(t)=t^2 − 8 t+ 16(See Figure 9.3-1.) The graph ofa(t) indicates that:
[−1, 7] by [−2.20]
Figure 9.3-1(1) The minimum acceleration occurs att=4 anda(4)=0.
(2) The maximum acceleration occurs att=0 anda(0)=16.
Example 3
The graph of the velocity function is shown in Figure 9.3-2.
0
–1123–2
–3
–41234v(t)vtFigure 9.3-2(a) When is the acceleration 0?
(b) When is the particle moving to the right?
(c) When is the speed the greatest?