Grade 12 Math: Rate of Change
This worksheet focuses on understanding and calculating the rate of change in various functions and contexts for Grade 12 students.
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Rate of Change Worksheet
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Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. The function f(x) = x^3 - 2x^2 + 5x - 1 describes the position of a particle at time x. Calculate the average rate of change of the particle's position from x = 1 to x = 3.
2. The instantaneous rate of change of a function at a specific point is equivalent to the slope of the line to the function's graph at that point.
3. If the derivative of a function f(x) is f'(x) = 2x - 3, then the instantaneous rate of change at x = 4 is .
4. Which of the following statements best describes the rate of change of the function shown in the graph below at x = 2?
The rate of change is positive.
The rate of change is negative.
The rate of change is zero.
The rate of change is undefined.
5. A car's distance d (in miles) from its starting point after t hours is given by the function d(t) = 50t + 10t^2. What is the car's instantaneous speed at t = 2 hours?
6. For a linear function, the average rate of change is always equal to the instantaneous rate of change.
True
False
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