Think you’ve got your head wrapped around Second Derivatives and Beyond? Put your knowledge to
the test. Good luck — the Stickman is counting on you!
Q. Which of the following functions has neither a global maximum or a global minimum?
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_1.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_2.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_3.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_4.png)
Q. A continuous function on an open interval
must have a global max and a global min.
cannot have a global max or a global min.
may or may not have a global max and/or a global min.
must have a global max if it has a global min.
Q. Which of the following statements about the function f (x) =
is correct?
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_1_latek_1.png)
f has a global max and a global min on the interval [-1,1].
f has a global max but no global min on the interval [-1,1].
f has a global min but no global max on the interval [-1,1].
f has neither a global max nor a global min on the interval [-1,1].
Q. What is the global maximum of the function
on the interval [-3,3]?
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_latek_1.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_latek_2.png)
0
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_latek_3.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_latek_4.png)
Q. Determine where the function f (x) = 4x4 + 2x is smallest on the interval [-2,2].
-2
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_latek_7.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_latek_8.png)
2
Q. Which of the following could be the start of a graph of the function f(x) = xex?
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_5.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_6.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_7.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_8.png)
Q. Which of the following graphs could be a correct representation of all intercepts, critical points, and inflection points of the function f(x) = x2 – 3x – 4?
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_10.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_10.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_11.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_8.png)
Q. If f ' is positive and f " is negative, what shape is the function f?
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_1_graphik_9.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_1_graphik_14.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_1_graphik_15.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_1_graphik_16.png)
Q. The function f looks like this: ![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_13.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_13.png)
Which of the following statements is true?
f ' is positive and f " is zero.
f ' is negative and f " is zero.
f ' and f " are both positive.
f ' and f " are both negative.
Q. The signs of the derivatives f ' and f " are as follows:
Use this information to fill in the graph of the function f :
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_16.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_17.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_18.png)
![](https://media1.shmoop.com/images/calculus/calc_hghderiv_quiz_3_graphik_19.png)