AP Calc AB Exam 1
**Section I: Multiple Choice**
1. The function \( f(x) = 3x^2 + 4x - 2 \) has a critical point at:
a) \( x = -2 \)
b) \( x = -\frac{2}{3} \)
c) \( x = \frac{2}{3} \)
d) \( x = 2 \)
2. The derivative of \( f(x) = e^x \) with respect to \( x \) is:
a) \( e^x \)
b) \( e^x + C \)
c) \( e^{-x} \)
d) \( e^{-x} + C \)
3. If \( f(x) = x^3 - 3x^2 + 2x + 1 \), then \( f'(x) \) is:
a) \( 3x^2 - 6x + 2 \)
b) \( 3x^2 - 6x + 1 \)
c) \( 3x^2 - 3x + 2 \)
d) \( 3x^2 - 3x + 1 \)
4. The definite integral \( \int_{0}^{2} (x^2 + 2x) \, dx \) is equal to:
a) 4
b) 6
c) 8
d) 10
5. The graph of \( f(x) = \sin(x) \) on the interval \( [0, 2\pi] \) is:
a) A line
b) A parabola
c) A circle
d) A sine wave
**Section II: Free Response**
6. Find the equation of the tangent line to the curve \( y = x^3 - 2x + 1 \) at the point where \( x =
1 \).
7. Evaluate the definite integral \( \int_{1}^{4} (2x - 1) \, dx \).
8. Find the derivative of the function \( y = \frac{3}{x} + e^x \).
