Mr. Orchard’s Math 142 WIR
1. Differentiate the following functions:
(a) e
6 x
4.4, 4.5, 5.1
(b) e 4 x
4 − 3 x
2
+ x
(c) e
12
(d) 3 x
(e) 5 ln( x ) − 2 x
5
Week 6

Mr. Orchard’s Math 142 WIR 4.4, 4.5, 5.1
2. Find the derivative of the following functions:
(a) ln(13 x )
Week 6
(b) log
3
(5 + 3 x 2 )
(c) log
88
(4 x 12 − 33 x + 2) + log
4
(2 x 3 )

Mr. Orchard’s Math 142 WIR 4.4, 4.5, 5.1
Week 6
3. Use the properties of logarithms to find F
0
( x ) where F ( x ) = ln ((5 x + 1) 4 (6 x − 1) 3 ).
4. Find the equation of the tangent line to the curve y = log
4
( x 4 x
3
) at the point (1 , 1).
5. If $1,600 is invested in a savings account with an interest rate of 6.5% compounded quarterly, how fast is the balance growing after 2 years?

Mr. Orchard’s Math 142 WIR 4.4, 4.5, 5.1
Week 6
6. If x = f ( p ) is a demand equation, write the formula for the elasticity of demand.
7. Use x =
√
180 − 2 p where x is the number of items demanded and dollars for the following questions.
p is the price in
(a) Find a formula for the price elasticity of demand.
(b) Is the demand elastic, inelastic, or unit elasticity at p = $20?
(c) Find the price so the demand will have unit elasticity. (Round to the nearest cent.)
(d) Give the interval where the demand is inelastic.

Mr. Orchard’s Math 142 WIR 4.4, 4.5, 5.1
Week 6
8. The demand curve for thingamajiggers is given by x = (96 − 3 p ) 2 (for 0 < p < 32), where p is the price per thingamajigger and x is the demand in weekly sales. Find the price the manufacturer should charge in order to maximize revenue.
9. The pair of price of running shoes is $76 and E (76) = 0 .
44. If the price is increased by
$4, then what is the approximate change in demand (rounded to the nearest hundredth of a percent).

Mr. Orchard’s Math 142 WIR
10. Below is the graph of G ( x ).
2
0.5
0
-0.5
1.5
1
-1
-1 0
4.4, 4.5, 5.1
1
(a) Find the critical values where G
0
( x ) = 0.
2
Week 6
3 4 5
(b) Find the critical values where G
0
( x ) does not exist.
(c) Find the x coordinates for the relative minima.

Mr. Orchard’s Math 142 WIR 4.4, 4.5, 5.1
Week 6
11. For the function f ( x ) = − 4 x 4 +72 x 2 − 36 find the points at which f has relative extrema.
(a) Relative maxima:
(b) Relative minima:

Mr. Orchard’s Math 142 WIR 4.4, 4.5, 5.1
Week 6
12. Suppose F ( x ) has a domain of all real numbers, and F
0
( x ) = ( x +2) 6 ( x − 6) 7 ( x − 9) 3 e x − 12 .
(a) Find the critical values of F ( x ).
(b) Find the intervals where F ( x ) is increasing.
(c) Find the x coordinates of the relative extrema of F ( x ).
i. Relative minima: ii. Relative maxima:

Mr. Orchard’s Math 142 WIR 4.4, 4.5, 5.1
13.
h ( x ) has a domain of all real numbers. Below is the graph of h
0
( x ).
7
4
3
2
6
5
1
0
-1
-2 -1 0 1 2
(a) Find the critical values of h ( x ).
Week 6
3 4
(b) Find the x values of the relative extrema of h ( x ).
i. Relative minima: ii. Relative maxima:
(c) Find the intervals where h ( x ) is decreasing.