123 MA Section A1
Arazyan, Spring 2008
Quiz#3
Student Name ___________Key_________ Discussion Section #___ BU ID#_______________
Show all your work for full credit. 1. (10 points) Find the following derivative :
d x2/3 2 dx e 2 x 3x
Solution:
d x2/3 2 dx e 2 x 3 x (2 / 3) x
1/ 3
( x 2 / 3 ) (e 2 x (e 2 x
2
2
3x) (e 2 x
2
( x 2 / 3 )(e 2 x 3x) 2
2
2
3x)
3x)
2
( x 2 / 3 )(4 xe2 x 3x) 2
2
3)
(e 2 x 2 3 x1 / 3 (e 2 x
2
(4 x 5 / 3e 2 x 3x) (e 2 x
2
3x 2 / 3 ) 3x) (10 2
2. points) The body temperature (in degrees Fahrenheit) of a patient t hours after being 4 given a fever-reduction drug is given by F (t ) 98 . Find F (x). Evaluate F (3) t 1 and F (3) . Write a brief verbal interpretation of these results. Solution: F (3) 100
F (t ) F (3) 2(t 1) 1 4
3/ 2
2 (t 1) 3
The body temperature of a patient 3 hours after being given a fever-reduction drug is 100 degrees Fahrenheit, and it decreases at the rate of -1/4 degrees per hour.