# Second Derivatives and Beyond

# Second Derivatives and Beyond: Are You Local? Quiz

Think you’ve got your head wrapped around

*? Put your knowledge to the test. Good luck — the Stickman is counting on you!***Second Derivatives and Beyond**Q. Which of the following functions has neither a global maximum or a global minimum?

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?*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]?

0

Q. Determine where the function

*f*(*x*) = 4*x*^{4}+ 2*x*is smallest on the interval [-2,2].-2

2

Q. Which of the following could be the start of a graph of the function

*f*(*x*) =*x**e*^{x}?Q. Which of the following graphs could be a correct representation of all intercepts, critical points, and inflection points of the function

*f*(*x*) =*x*^{2 – }3*x*– 4?Q. If

*f*' is positive and*f*" is negative, what shape is the function*f*?Q. The function

*f*looks like this: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*: