1. Answer the questions from the graph of y = F(x) drawn below. (Each hash mark along the
axes represents 1 unit.)
a. For which x is F'(x) = 0 ?
b. Estimate F'(5)
c. Estimate F'(-1).
d. F'(x) < 0 on which interval(s)?
e. F'(x) > 0 on which interval(s)?
2. The graph drawn below gives the position s(t) (cm) of a particle at time t (sec). Use the
graph to answer the questions below.
a. The particle is moving forwards (in the positive direction) for which time interval(s)?
b. The particle is moving backwards (in the negative direction) for which time interval(s)?
c. The velocity of the particle is zero at what time(s)?
d. Use the graph to estimate v(2), the velocity at time t = 2.
e. Provide the units of v(t) and a(t), the velocity and acceleration functions of the particle.
f. Sketch a graph of v(t).
note: each unit along x-axis represents 1 sec. each unit along y-axis represents 1 cm.
3. The graph drawn below gives the velocity v(t) (m/hr) of a particle at time t (hr). Use the
graph to answer the questions below.
a. The particle is moving forwards (in the positive direction) for which time interval(s)?
b. The particle is moving backwards (in the negative direction) for which time interval(s)?
c. The velocity of the particle is zero at what time(s)?
d. The critical value(s) of v(t) occur at what time(s)? What is happening to the particle at
the critical value(s) of v(t)?
e. Use the graph to estimate a(-2), the acceleration at time t = -2.
f. Provide the units of s(t) and a(t), the position and acceleration functions of the particle.
note: each unit along x-axis represents 1 sec. each unit along y-axis represents 10 cm/sec.