Math 131 Week in Review Sections 3.4, 3.7, 3.8 and 3.9
J. Lewis
Use the chain rule when needed to find the derivative of each function.
1.
f ( x )  ( x  1) ( 5 x  1)
2.
f ( x)  7e
3.
 x 2 ( x 3  2 x )1 4 
f ( x )  ln 

2
5
 ( x  1)

4.
f ( x )  log 3 ( 5 x  2 x )
5.
f ( x )  (ln x )
6.
a ) f ( x )  ln | sec x |
7.
f ( x )  ln | sec x  tan x |
8.
f ( x )  cot ( x )
9.
f ( t )  Pe
2
3
x5 x
3
4
2
2
3
2
b ) f ( x )  ln | cos x |
2
rt
Find the derivative of f with respect to t. Find the approximate change in f if t
increases by 1. Find the approximate % change in f if t increases by 10%.
10.
Use differentials or linearization to approximate a) a )
11. The surface area of a sphere is S  4  r
2
5
33
b)
5
30
Find the approximate % change in S
if r increases by 5%.
12. This is #24 in 3.8 of the textbook by Stewart.
The number of yeast cells in a laboratory culture increases rapidly initially but levels off eventually. The
population is modeled by the function n  f ( t ) 
a
1  be
 0 .7 t
.
At time t=0, the population is 20 cells and is increasing at a rate of 12 cells per hour. Find the values of a
and b. According to this model, what happens to the yeast population in the long run?
Use the calculator to approximate the time when the growth rate begins to decrease.
Graph the derivative of f(t) in the calculator.