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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Calculate the average rate of change of $f(x) = 4x - 3$ from $x = 2$ to $x = 5$.
💡 Hint: Use the AROC formula with $a = 2$ and $b = 5$.
Question 2
Easy
What is the slope of the secant line for $f(x) = x^2$ from $x = 0$ to $x = 2$?
💡 Hint: Calculate using the AROC formula.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for average rate of change?
- $$\\frac{f(b) + f(a)}{b + a}$$
- $$\\frac{f(b) - f(a)}{b - a}$$
- $$f'(x)$$
💡 Hint: Think about how we derive the slope between two points.
Question 2
True or False: The tangent line gives us the average rate of change.
- True
- False
💡 Hint: Remember the difference between average and instantaneous.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
A car travels a distance described by $d(t) = 4t^2 + 2t$ km in hours. Find the average speed from $t = 1$ to $t = 3$.
💡 Hint: Use the AROC formula on distance.
Question 2
Given the function $g(x) = x^3 - 3x^2 + 4$, calculate the IROC at $x = 1$ and interpret its significance.
💡 Hint: Differentiate $g(x)$ then evaluate at $x = 1$.
Challenge and get performance evaluation