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Second Derivatives and Beyond

Second Derivatives and Beyond

Second Derivatives and Beyond: Are You Local? Quiz

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?


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  (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 (x) = 4x4 + 2x 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) = xex?


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?


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


Q. The function f looks like this:

Which of the following statements is true?



' is positive and " is zero.
' is negative and " is zero.
' and " are both positive.
' and " are both negative.
Q. The signs of the derivatives ' and " are as follows: 

   

 Use this information to fill in the graph of the function :

 



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