AP Calculus AB: Chapter 3 Practice Test
This content provides practice with calculating the average rate of change and the slope of secant lines for various polynomial functions. It also includes examples of finding derivatives using both the definition of the derivative and standard differentiation rules, as well as interpreting velocity from position functions in motion problems.
What is the average rate of change of the function y = 2x ^2 + 3 between x = 2 and x = 4?
12
Key Terms
What is the average rate of change of the function y = 2x ^2 + 3 between x = 2 and x = 4?
12
What is the slope of the secant line of the function y = 4x ^2 − 2x + 1 between x = 3 and x = 6?
34
What is the average rate of change of the function y = 4x^ 3 − 2 between x = 2 and x = 4?
112
What is the slope of the secant line of the function y = −2x ^2 + 3x − 1 between x = x1 and x = x2?
−2x1 − 2x2 + 3
The position of a car at time t is given by the function p (t) = t^ 2 − 4t − 18. Where will the car be when its velocity is 10? Assume t ≥ 0.
3
Apply the definition of the derivative to differentiate the function f (x) = 6.
0
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| Term | Definition |
|---|---|
What is the average rate of change of the function y = 2x ^2 + 3 between x = 2 and x = 4? | 12 |
What is the slope of the secant line of the function y = 4x ^2 − 2x + 1 between x = 3 and x = 6? | 34 |
What is the average rate of change of the function y = 4x^ 3 − 2 between x = 2 and x = 4? | 112 |
What is the slope of the secant line of the function y = −2x ^2 + 3x − 1 between x = x1 and x = x2? | −2x1 − 2x2 + 3 |
The position of a car at time t is given by the function p (t) = t^ 2 − 4t − 18. Where will the car be when its velocity is 10? Assume t ≥ 0. | 3 |
Apply the definition of the derivative to differentiate the function f (x) = 6. | 0 |
Differentiate the function f (x) = 2x. | 2 |
Evaluate f′(x) if f(x)=√x+1. | 1/2√x+1 |
Find the derivative of the function: f (x) = 2x ^2. | 4x |
Evaluate the following as true or false: The derivative of a function f (x) at a point x0 is equal to the equation of the line tangent to f (x) at the point x0. | false |
Find the slope of a line tangent to f (x) = x^3 at the point (x, f (x)). | 3x^2 |
Find the equation (in point-slope form) of the line tangent to f(x)=3x^2−2 at the point x=−3. | y−25=−18(x+3) |
The instantaneous rate of change of a ball (in ft/s) is given by f′(x)=1√x. When was the ball traveling 2 ft/s? | 1/4 sec |
True or false? | false |
Consider the function y = x^ 2 − x + 7. What is the equation of the tangent line at x = 2? | y − 9 = 3 (x − 2) |
The position of a car at time t is given by the function p (t) = t ^2 − 2t − 4. What is the velocity at t = 2? Assume t ≥ 0. | 2 |
The position of a car at time t is given by the function p (t) = t ^2 + 2t − 4. What is the velocity when p (t) = 11? Assume t ≥ 0. | 8 |
The position of a car at time t is given by the function p (t) = t ^2 − 3t − 6. At what time will the velocity of the car be 7? Assume t ≥ 0. | 5 |
What is the derivative of the function f (x) = 4x ^3 − 2 at x = 4? | 192 |
What is the derivative of the function f = 2x^ 2 + 3 at x = 2? | 8 |