Practice Secant Lines And Tangent Lines (1.6) - Rates of Change - IB 10 Mathematics – Group 5, Calculus

Practice: Secant Lines and Tangent Lines

Lesson 1.6Rates of Change

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What is the average rate of change of $f(x)=x^2$ from $x=2$ to $x=4$ ?
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Use the average rate of change formula.
Question 2.
Define a secant line using your own words.
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Think about its connection to the average rate of change.
3Question 3.
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) \$
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Remember, it's about connecting two points.
4Question 4.
True or False: A tangent line can intersect a curve at multiple points.
- True
- False
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Think about how tangent lines behave.
Question 5.
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 $x=1$ .
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Calculate points and slopes for both lines before drawing!
Question 6.
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 $x=1$ .
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Start with the secant's slope first!

4 more questions in this section. Enroll free to practise them all.