QUIZ 6
Name
Find each of the following derivatives. Some are implicit, some are standard, so make sure your nal
dy
answer is in the form y (or f (x) or dx ) = formula.
1. y = x3 ex + 2
2. f (t) = (3t2 + t)5 (5t 8)
3. y = ln (3x4 x2 + 5)
4. x2 + xy = y 2 5
EXAM 1
Math 106
September 23, 2010
Name
You must show all your work. Partial credit will be given.
1. The following table shows the amounts spent on reducing sizes of rst-grade through thirdgrade public school classes in a certain state.
Year
1988
1990
19
QUIZ 5
Name
1. Calculate the average rate of change of q (x) = 3x2 + 1 on the interval [1, 2].
2. Find a derivative formula for the equation g(x) = (3x2 +
x)(x2 x)3 .
3. Use the (limit) denition to nd the derivative of f (x) = 3(x 2)2 at x = 3.
4. Find th
EXAM 3
Math 106
January 10, 2011
Name
You must show all your work. Partial credit will be given.
1. Find each of the following quantities: (8 pts each)
(a)
5x3 4x + 2x3 dx
(b)
6x2 (x3 + 1)3 dx
(c)
4u3 15u
du
u2
(d)
3x x3 dx
4
5
2
xx
(e)
dx
3
2t dt
(f)
2
2
QUIZ 3
Name
1. Find the derivative for each of the following functions:
(a) g(x) = 2x + 4x2
(b) h(t) = 15t4 17t2 + 300t
(c) y = 1 x7 3x2
2
(d) g(t) = (3t2 1)(5t7 8t + 1)
(e) f (x) =
3x4 x
x2 + 1
EXAM 2
Math 106
November 3, 2010
Name
You must show all your work. Partial credit will be given.
1. Find a derivative formula for each of the following equations. (You may use any method.) (7
pts each)
(a) g(x) = 3x2 5x7 + 18
(b) f (x) = x5 + 2x2 3x1
(c)
QUIZ 2
Name
1. Find the derivative of the function g(x) = x2 4. (Use the limit denition of the derivative.)
2. Determine the equation of the line tangent to f (x) = (x 3)2 at (3, 0).
QUIZ 6
Name
1
1. Find all the critical values of the function f (x) = 3x 3 x.
2. Build a sign chart for the function g(t) = t3 1.
3. Find the absolute maximum and the absolute minimum for C (p) = 4p3 12p + 7 on the
interval [3, 3].
QUIZ 8
Name
1. Find the derivative for each of the following:
(a) f (x) = (x2 3)2 (3x 4x3 )3 .
(b) h(t) = et ln (5x2 3x)
2. Based on data from 1999 to 2001, the net sales (revenue) of Pepsi-Cola North America may
be modeled by
R(t) = 65.5t2 749.5t + 2605
QUIZ 12
Name
1. Find each of the following:
x4 3x4 + x1 dx
(a)
1
3 5
3t2 et
(b)
dt
0
1
(c)
1
5t2 3t
dt
t
2. Use a right hand sum to estimate the area under the curve y = 3x2 2x on the interval [0, 3]
using n = 2.
QUIZ 11
Name
1. Find each of the following:
(a)
3x2 5x1 + x3 dx
(b)
3
(2t 1)
dt
t+5
t2
3
(3t ) dt
(c)
3
2. Use a left hand sum to estimate the area under the curve y = x2 2x on the interval [2, 5]
using n = 4.
QUIZ 10
Name
1. Find the family of antiderivatives for each of the following functions:
(a) f (x) = 3x x3
(b) g(t) = 4t2 + 2t1 + 1
2. Find
5u2 4u + 1
du
u2
QUIZ 7
Name
1. Find each of the following derivatives. Some are implicit, some are standard, so make sure
dy
your nal answer is in the form y (or f (x) or dx ) = formula.
2
(a) y = e3x ln (x)
(b) f (t) =
(3t4 t2 + 1)4
3t2 1
2. Find the second derivative o
QUIZ 9
Name
1. Find the derivative for each of the following: (one is implicit)
(a) f (x) = 3x + ln (x2 x).
(b) 9x2 y 3 = 0
2. Find the absolute maximum and the absolute minimum for h(t) = t3 6t2 on the interval
[1, 7].
3. Find the second derivative for g
QUIZ 1
Name
1. Calculate the average rate of change of q (x) =
x + 2 on the interval [0, 6].
2. Calculate the average rate of change in the temperature between 11:00am and 3:00pm.
Time of Day
11:00am
1:00pm
3:00pm
Temperature ( F)
68
73
75
f (a + h) f (a)