Assignment 1:
Name:____________________________ Date: _____________
Answer the following problems below and show your complete solution. Each problem
will give you points based on the rubrics. Total Score: 50
A. Find the value or values of x for which the given function has a maximum or a minimum
value.
1. � = 8�3 − 9�2 + 1
ANS: max: x = 0 | min: x = 3/4 or 0.75
2. � = 4�−1 + �
ANS: max: x = -2 | min: x = 2
3. � = 2�3 − 9�2 + 12� + 4
ANS: max: x = 1 | min: x = 2
5. � = �3 − 3�2 + 3
ANS: max: x = 0 | min: x = 2
4. � = �2 � − 1
2
ANS: max: x = 1/2 or 0.5 | min: x = 0 & x = 1
B. Find the value or values of c that satisfy the equation
�(�) − �(�)
= �'(�)
�−�
in the conclusion of the Mean Value Theorem for the functions and intervals below.
1. �(�) = �2 + 2� − 1, [0, 1]
ANS: c = 1/2
2. f ( x)  x 2 3 , [0, 1]
ANS: c = 8/27
1 1 
3. f ( x)  x  ,  , 2
x 2 
ANS: c = 1
4. f ( x)  x  1, [1, 3]
ANS: c = 3/2
5. f ( x)  x 3  x 2 , [-1, 2]
ANS: c 
1 7
3