Practice Graphical Interpretation (1.5) - Rates of Change - IB 10 Mathematics – Group 5, Calculus

Practice: Graphical Interpretation

Lesson 1.5Rates of Change

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10 questions

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6 sample questions

Question 1.
Find the average rate of change of f(x) = 5x - 3 from x = 2 to x = 4.
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Use the slope formula between the two points.
Question 2.
What is the slope of the line connecting points (3, 6) and (5, 10)?
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Apply the slope formula.
3Question 3.
What does the slope of a secant line represent?
- Average Rate of Change
- Instantaneous Rate of Change
- Both Average and Instantaneous Rate of Change
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Remember the definition of secant lines.
4Question 4.
The instantaneous rate of change at a point is defined by what mathematical operation?
- True
- False
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Think about the definition of a derivative.
Question 5.
Given the function g(x) = x^2 + 3x, calculate both the average rate of change from x = 1 to x = 4 and the instantaneous rate of change at x = 3.
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Use the AROC formula for the first part, then find the derivative.
Question 6.
For the function y = x^3 - 3x + 4, find the average rate of change between x = 0 and x = 2 and analyze the behavior of the function graphically.
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Compute the function values at both points and find the slope.

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