MCV4U
Assignment 1 – Rate of Change
Overall Expectation(s): Demonstrate an understanding of rate of change by making connections
between average rate of change over an interval and instantaneous rate of change at a point,
using the slopes of secants and tangents and the concept of a limit.
Learning Goal(s): I will be able to
• Find the average rate of change between an interval.
• Estimate the IROC numerically.
• Identify what is IROC over AROC and explain
• Relate finite differences to AROC
Success Criteria: I am successful when
• I can solve the problems independently.
• I know how to calculate AROC and estimate IROC
• Explain what is AROC and IROC
Assignment Description: This assignment expects you to demonstrate an understanding
about rate of change in functions.
1. (KU: 6) Find the average rate of change from x = 0 to x = 4 for each. Also, estimate the
instantaneous rate of change at x = 3 for each.
a. 𝑓(𝑥) = −𝑥 2 + 3𝑥 − 4
b.
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c.
x
y
0
5
1
7
2
12
3
20
4
31
5
45
2. (KU: 2) Determine the average rate of change between the points (-9.4,5.2) and (4.8,-1.6).
3. (KU: 2) Estimate the instantaneous rate of change at the tangent point indicated on the
graph.
3. (T:5, C -5) Determine if each situation represents AROC or IROC. Explain your choice.
a) When water is poured into a cylindrical glass, the water level increases at 2.5 cm/s.
b) Jordan grew 8 cm in 15 months.
c) At an altitude of 8000m, the plane’s speed was 820km/h.
d) The temperature of the pool water dropped 5 degrees overnight.
e) The price of gas increased 20% in 3 h.
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4. (A:10) The table shows the height of a golf ball every second after it was hit.
a) Graph the data.
b) What type of function does the graph represent? Use finite differences to verify your
answer.
c) What do finite differences tell you about the AROC height of the ball?
d) When was the instantaneous rate of change of the ball positive? Negative?
e) What is the maximum height of the ball? What is the instantaneous rate of change at
this point?
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