Practice Definition (1.3.1) - Rates of Change - IB 10 Mathematics – Group 5, Calculus
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Definition

Practice - Definition - 1.3.1

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Practice Questions

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Question 1 Easy

Find the AROC of \(f(x) = 2x + 3\) from \(x = 1\) to \(x = 5\).

💡 Hint: Use the formula \\( \\frac{f(b) - f(a)}{b - a} \\).

Question 2 Easy

For \(f(x) = x^2\), determine the AROC from \(x = 0\) to \(x = 2\).

💡 Hint: Calculate \\(\\frac{f(2) - f(0)}{2 - 0}\\).

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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)\\)

💡 Hint: Think about what AROC measures.

Question 2

True or False: The IROC measures the change of a function over an interval.

True
False

💡 Hint: Remember the difference between AROC and IROC.

2 more questions available

Challenge Problems

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Challenge 1 Hard

Given the function \(f(x) = \ln(x)\), find the AROC from \(x = 1\) to \(x = e\).

💡 Hint: Remember that \\(\\ln(e) = 1\\) and \\(\\ln(1) = 0\\).

Challenge 2 Hard

If the height of a rocket is described by \(h(t) = 4t^2 + 2t\), calculate the IROC when \(t = 3\).

💡 Hint: Differentiate the height function to find the rate of change.

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