Free AP Calculus AB Tests

AP Calculus AB Practice Tests

Logarithms
Limits
Derivatives Part 1
Derivatives Part 2
Derivatives Part 3
Idefinite & Definite Integrals
Riemann Sums, Trapezoidal…
Trigonometric Integrals
Applications of Calculus
Differential Equations

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AP Calculus AB Practice Test: Derivatives Part 3

This is Part 3 of our AP Calculus AB unit test on derivatives. These questions cover tangent lines, mean value theorem, Rolle’s theorem, and inverses of functions. Practicing the application of derivatives theorems to a function will help you solve complicated problems on the AP exam asking you to analyze the behavior of a given function.

Next: AP Calculus AB Idefinite & Definite Integrals

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Free AP Calculus AB Tests

AP Calculus AB Practice Tests

More AP Calculus AB Practice Exam

AP Calculus AB Practice Test: Derivatives Part 3

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1. Question

What is the slope of the tangent line at $x = 2$ for the function below.

$f(x) = \ln(2x) + x^2$

2. Question

Which of the following is the equation for the line tangent to the function below at $x = 3$.

$f(x) = \sin\left(\dfrac{π}{2}x\right) +6x^3$

3. Question

Which of the following equations is the equation of the line tangent to the graph below at $x = 0$.

$f(x) = \dfrac{1}{x^3 + 4x + 6}$

4. Question

Using the mean value theorem, identify a value for $c$ which the slope of the line tangent to $f(x)$ at $x = c$ is equal to the average rate of change of the function on the given domain.

$f(x) = x^3 + 3x + 2$ $−1 ≤ x ≤ 3$

5. Question

Using mean value theorem, identify a value $x = c$ such that the slope of the line tangent to $f(x)$ at $c$ is equal to the average rate of change of the function on the given domain.

$f(x) = \sin^{−1}(x)$ $−\frac{1}{2} ≤ x ≤ \frac{1}{2}$

6. Question

Identify if the function below can be applied to mean value theorem, and, if so, identify the value $c$ such that the slope of the line tangent to $f(x)$ at $x = c$ is equal to the average rate of change of the function on the given domain.

$f(x) = \frac{1}{x}$ $−1 ≤ x ≤ 3$

7. Question

Using Rolle’s Theorem, identify a value $x = c$ such that the slope of the line tangent to $f(x)$ at $c$ is equal to the average rate of change of the function on the given domain.

$f(x) = x^2 + 3$ $−2 ≤ x ≤ 2$

8. Question

Using Rolle’s Theorem, identify a value $x = c$ such that the slope of the line tangent to $f(x)$ at $c$ is equal to the average rate of change of the function on the given domain.

$f(x) = \ln(x^2)$ $−1 ≤ x ≤ 1$

9. Question

For the inverse of the function below, what is the slope of the line tangent to the curve when $x = 6?$

$y = x^2 + 2x + 3$, for $x \ge −1$

10. Question

For the inverse of the function below, what is the slope of the line tangent to the curve when $x = 6?$

$y = \ln(x^6)$

Next: AP Calculus AB Idefinite & Definite Integrals