Practice Worked Examples (1.8) - Rates of Change - IB 10 Mathematics

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6 sample questions

Question 1.
What is the average rate of change of $f(x) = 3x^2 - 2x$ from $x = 1$ to $x = 4$ ?
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Use the formula \$ \\frac{f(4) - f(1)}{4 - 1} \$.
Question 2.
Find the instantaneous rate of change of $s(t) = 4t^2 - t + 1$ at $t = 2$ .
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Calculate the derivative and evaluate it at \$ t = 2 \$.
3Question 3.
What is the formula for average rate of change?
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Think about the change in the function divided by the change in the interval.
4Question 4.
True or False: The instantaneous rate of change is the derivative of the function.
- True
- False
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Consider how we define the derivative mathematically.
Question 5.
A car's position over time is given by $s(t) = 5t^3 - 4t^2 + 2t$ . What is the average rate of change from $t = 1$ to $t = 3$ ?
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Evaluate the function at both time points!
Question 6.
Given the function $f(x) = e^x$ , find the instantaneous rate of change at $x = 0$ .
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What is the derivative of the exponential function?

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