Name: 
 

03-02-Higher Derivatives and Concavity



Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

Find the second derivative of the following function.

mc001-1.jpg
a.
mc001-2.jpg
d.
mc001-5.jpg
b.
mc001-3.jpg
e.
mc001-6.jpg
c.
mc001-4.jpg
f.
mc001-7.jpg
 

 2. 

Find the requested derivative:

  mc002-1.jpg
a.
mc002-2.jpg
d.
mc002-5.jpg
b.
mc002-3.jpg
e.
mc002-6.jpg
c.
mc002-4.jpg
f.
mc002-7.jpg
 

 3. 


The function mc003-1.jpg is shown in the graph (the second derivative).



Given mc003-2.jpg is differentiable for all real values of  x which of the number lines correctly describe where mc003-3.jpg is concave up or concave down.
mc003-4.jpg
a.

mc003-5.jpg
b.

mc003-6.jpg
c.

mc003-7.jpg
d.

mc003-8.jpg
 

 4. 

Which is the only graph below that appears to have no points of inflection?
a.
mc004-1.jpg
c.
mc004-3.jpg
b.
mc004-2.jpg
d.
mc004-4.jpg
 

 5. 

Consider the following values of  mc005-1.jpg such that  mc005-2.jpg

mc005-3.jpg

If  mc005-4.jpg is differentiable for all real values of  x, what is the minimum number of inflection points that mc005-5.jpg must have on the interval mc005-6.jpg?
a.
0
d.
3
b.
1
e.
4
c.
2
f.
5
 



 
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