Practice Test 4 - AP Calculus AB

20 questions. Answer them in any order, then submit to see your score and every explanation.

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1. Based on the description of the graph of $f(x)$, what is $\lim_{x \to 3} f(x)$?
2. A particle's acceleration is positive at $t=3$ and its velocity is zero at $t=3$; which is correct at $t=3$?
3. For $f$ with $f'(x)=(x+2)(x-1)^2$, on which interval(s) is $f$ increasing?
4. A bacterial culture increases by $1210^6$ cells in $3$ hours; what is the average growth rate?
5. A function satisfies $\dfrac{dy}{dx}=x y$. What is the general solution for $y$?
6. For $f(x)=\cos(x^2)$, what is the second derivative $f''(x)$?
7. What is the correct volume integral setup if the base is bounded by $y=4-x^2$ and $y=0$ on $[-2,2]$ with rectangular cross sections perpendicular to the $x$-axis of height $3$?
8. Let $f(x) = \frac{x^4}{4} - \frac{x^2}{2} + 5$. For which value of $x$ does $f'(x) = 0$?
9. If $f(x) = 4\sin(x) - e^x + 1$, what is the value of $f'(0)$?
10. For $\lambda(x)=\begin{cases}1,&x\le2\\3,&x>2\end{cases}$, what type of discontinuity does $\lambda$ have at $x=2$?
11. A company's revenue is $R(t)=2000+300t$ dollars after $t$ weeks; what is the weekly revenue rate?
12. A continuous function $W$ satisfies $W(-4)=\!-2$ and $W(-1)=6$. Which must exist?
13. What is the fundamental algebraic obstacle that makes it impossible to directly compute an instantaneous rate of change without using the concept of a limit?
14. A control system uses $h(x)=\arctan(5x+4)$. What is $h'(x)$?
15. Define $F(x)=\int_{-2}^{x}\sqrt{1+t^4}\,dt$. What is $F'(x)$?
16. A function $v$ is continuous on $[-4,4]$ and satisfies $v(-4)=2$ and $v(4)=2$. Which statement must be true?
17. If $h'(1)=0$ and $h$ is concave down on $(0,2)$, what is the classification of $x=1$?
18. A slope field is for $\frac{dy}{dx}=x-y^2$. At the point $(0,2)$, the solution curve is locally
19. The temperature of a chemical solution is $T(t)$ °C after $t$ minutes. What is the meaning of $T'(7)$?
20. A rumor spreads so that the rate $\dfrac{dP}{dt}$ is proportional to $P(1000-P)$; which differential equation models this?

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