Mat 116 – Ms. Bui
Quiz 3: Section 11.1 – 11.4
Name _____________________
Date _____________________
Please show your work step by step for full credits and circle your final answers.
From 1 to 16, find the derivative for each of the following function then simplify where indicated
YOU CAN OMIT ONE PROBLEM (1-16 only)
1) f(x) =
1 x
e
2
2) f(x) =  5 ln x
3) f(x) = e x  x  ln x
4) f(x) = ln x4
5) f(x) = log 3 x
6) f(x) = 7 x
7) f(x) = -9x + ln (8x)
8) f(x) = x2 ex [factor your final answer]
9) f(x) =
3x  2
[simplify]
x3
10) f(x) = 2 x x [simplify and factor]
11) f(x) = ( x 6  10) 2 [simplify]
12) f(x) = ln(3x - 2)8
13) f(x) = xe3x [simplify and factor]
14) f(x) =
15) f(x) =
1
[simplify]
2
x  3x
16) f(x) =
[simplify]
x 3  5 [simplify]
x 10
2  3x
[simplify]
17) Price-demand equation. The number x of popcorn makers people are willing to buy per
week at a price of $p is given by x = 1000  40 p  75
with 20 ≤ p ≤ 100
A) Find dx/dp
B) Find the demand when the price is $25
C) Find the instantaneous rate of change of demand with respect to price (dx/dp) when the price
is $25.
18) Provident Bank offered a 10-year CD that earns 2.15% compounded continuously
A) If $50,000 is invested in this CD, how much will it be worth in 12 years?
B) How long will it take for the account to be worth $60,000?
Number 19 and 20, you may OMIT ONE PROBLEM
19) Some developed nations have population doubling times of 300 years. At what continuous
compound rate (in %) is the population growing?
20) The continuous compound rate of decay of carbon-14 per year is r = -0.0001532. How long
will it take a certain amount of carbon-14 to decay to half the original amount?
21) Given f(x) = (3x – 1)2
A) Find the equation of the line tangent to the graph at x = 2.
B) Find the value(s) of x where the tangent line is horizontal.
Chapter 11- FORMULA SHEET
•
If f (x) = ex, then f ’(x) = ex
1
• If f (x) = ln x, then f ’(x) =
x
• If f (x) = ax, then f ’(x) = ax ln a
• If f (x) = log a x , then f ’(x) =
1
x ln a
• If f (x) = U · V, then f ’(x) = U’ V + V’ U
• If f (x) =
U
, then f ’(x) =
V
U ' V  V 'U
V2
• If f (x) = kUn, then f ’(x) = kn Un-1 U’
Product Rule
Quotient Rule
General Power Rule
Chain Rule
Future value A = P e rt for compounded continuously
P: principle, r: interest rate, t: number of years