AP Calculus Foundations Worksheet

AP Calculus Foundations Worksheet

Read each question carefully and provide your best answer. Show all your work for full credit.

1. What is the value of the limit: $\lim_{x \to 2} \frac{x^2 - 4}{x - 2}$?

2. The derivative of $f(x) = x^3$ is $f'(x) = \text{ }$.

3. If $y = \sin(x)$, then $\frac{dy}{dx} = \text{ }$.

4. Find the equation of the tangent line to the curve $y = x^2 + 1$ at the point $(1, 2)$.

5. A function is continuous at a point if its limit exists at that point, the function is defined at that point, and the limit equals the function's value at that point.

6. Consider the function $f(x) = x^3 - 3x^2$. Find the critical points, intervals of increasing/decreasing, and local extrema. Sketch the graph of the function.