Practice Example (1.3.2) - Rates of Change - IB 10 Mathematics – Group 5, Calculus

Practice: Example

Lesson 1.3.2Rates of Change

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6 sample questions

Question 1.
Find the average rate of change of f(x) = x² from x = 0 to x = 2.
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Evaluate the function at both endpoints first.
Question 2.
Find the average rate of change of f(x) = 5x + 1 from x = 2 to x = 6.
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For a straight line, the AROC is always the gradient.
3Question 3.
Which expression gives the average rate of change of f from x = a to x = b?
- (f(b) − f(a)) / (b − a)
- (f(b) + f(a)) / (b + a)
- (b − a) / (f(b) − f(a))
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Think rise over run.
4Question 4.
What is the average rate of change of f(x) = x² from x = 1 to x = 3?
- 2
- 4
- 8
- 9
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Divide the change in y by the change in x.
Question 5.
The volume of water in a tank is V(t) = 200 − 4t² litres, where t is the time in minutes and 0 ≤ t ≤ 7. Find the average rate of change of V from t = 1 to t = 5 and interpret it.
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A negative rate of change means the quantity is decreasing.
Question 6.
Show that the average rate of change of f(x) = x² from x = a to x = b is a + b, and use this to find the AROC from x = 1.5 to x = 4.5.
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Factorise b² − a² as a difference of two squares.

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