Download test_ch11

Mat 116
Name _____________________
Review: Chapter 11 (11.1 – 11.4)
Date _____________________
Please show your work step by step for credits and circle your final answer.
(If you only give me the final answer, you may not receive any points for that).
From 1 to 16, find the derivative for each of the following function then simplify (factor is
not necessary but do not leave any answer with negative exponents
#1 and 2: 3 points each;
#3 - #16: 4 points each
1
1) f(x) =  e x
3
2) f(x) = 4 ln x
3) f(x) = e x  x  ln x
4) f(x) = ln x3
5) f(x) = log 2 x  99
6) f(x) = 3 x  e x
7) f(x) = 10x + ln (10x)
8) f(x) = x3ex
9) f(x) =
2x  3
x2
10) f(x) = ( x  1)2 x
11) f(x) = ( x 4  1)2
12) f(x) = ln(2 - 3x)3
13) f(x) = xe2x
14) f(x) =
x2  4
16) f(x) =
(2 x  1)2
2  3x
15) f(x) =
1
2
x  4x  4
17) Price-demand equation. The number x of stereo speakers people are willing to buy per
week at a price of $p is given by x = 1000  60 p  25
with 20 ≤ p ≤ 100
A) Find dx/dp [4points]
B) Find the demand when the price is $75 (may use G.C) [3points]
C) Find the instantaneous rate of change of demand with respect to price when the price is $75.
(may use G.C) [3points]
18) Provident Bank offered a 10-year CD that earns 5.51% compounded continuously
A) If $10,000 is invested in this CD, how much will it be worth in 12 years? [5points]
B) How long will it take for the account to be worth $15,000? [5points]
19) Some developed nations have population doubling times of 200 years. At what
continuous compound rate (in %) is the population growing? [5points]
20) The continuous compound rate of decay of carbon-14 per year is r = -0.0001238. How
long will it take a certain amount of carbon-14 to decay to half the original amount?
[5points]
21) Given f(x) = (2x – 1)3
A) Find the equation of the line tangent to the graph at x = 1. [5points]
B) Find the value(s) of x where the tangent line is horizontal. [3points]