Practice Definition (1.3.1) - Rates of Change - IB 10 Mathematics

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6 sample questions

Question 1.
Find the AROC of $f(x) = 2x + 3$ from $x = 1$ to $x = 5$ .
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Use the formula \$ \\frac{f(b) - f(a)}{b - a} \$.
Question 2.
For $f(x) = x^2$ , determine the AROC from $x = 0$ to $x = 2$ .
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Calculate \$\\frac{f(2) - f(0)}{2 - 0}\$.
3Question 3.
What is the formula for Average Rate of Change?
- \$\\frac{f(b) - f(a)}{b - a}\$
- \$\\lim_{h \\to 0} \\frac{f(a + h) - f(a)}{h}\$
- \$f'(x)\$
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Think about what AROC measures.
4Question 4.
True or False: The IROC measures the change of a function over an interval.
- True
- False
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Remember the difference between AROC and IROC.
Question 5.
Given the function $f(x) = \ln(x)$ , find the AROC from $x = 1$ to $x = e$ .
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Remember that \$\\ln(e) = 1\$ and \$\\ln(1) = 0\$.
Question 6.
If the height of a rocket is described by $h(t) = 4t^2 + 2t$ , calculate the IROC when $t = 3$ .
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Differentiate the height function to find the rate of change.

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