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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the average rate of change of \( f(x)=x^2 \) from \( x=2 \) to \( x=4 \)?
💡 Hint: Use the average rate of change formula.
Question 2
Easy
Define a secant line using your own words.
💡 Hint: Think about its connection to the average rate of change.
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 the slope of a secant line?
- \\( \\frac{f(b) - f(a)}{b - a} \\)
- \\( \\frac{f(a + h) - f(a)}{h} \\)
- \\( f'(a) \\)
💡 Hint: Remember, it's about connecting two points.
Question 2
True or False: A tangent line can intersect a curve at multiple points.
- True
- False
💡 Hint: Think about how tangent lines behave.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Sketch the graph of \( f(x) = 2x^2 - 3x + 1 \) and show both a secant line between \( x=0 \) and \( x=2 \) and a tangent line at \( x=1 \).
💡 Hint: Calculate points and slopes for both lines before drawing!
Question 2
For \( f(x) = x^3 - 2x + 1 \), determine the coordinates of the point on the curve where the tangent line has the same slope as the secant line from \( x=-1 \) to \( x=1 \).
💡 Hint: Start with the secant's slope first!
Challenge and get performance evaluation