Math 1431
Section 14819
TTh 10-11:30am 100 SEC
Bekki George
bekki@math.uh.edu
639 PGH
Office Hours:
11:30am – 12:30pm TTh and by appointment
Class webpage:
http://www.math.uh.edu/~bekki/Math1431.html
Test 2 scheduler is open!
Save your confirmation email. Note that if you miss your time or
are late, you will lose your seat and may get a 0 on the test.
Your final exam does replace your lowest test grade.
Test 2 covers sec 1.2-3.2
Practice Test 2 counts as bonus (5% added to test 2).
Review sheet will be turned in as your lab quiz grade on Oct 1.
Popper05
1. What is the 50th derivative of f  x   sin x ?
Rates of Change Examples:
x(t) is the position function
v(t) is the velocity function, v(t)=x’(t)
a(t) is the acceleration function, a(t)=v’(t)=x’’(t)
1. A body moves along a horizontal line according to
x(t) = t3 – 9t2 + 24t, where t is in seconds.
a) When is x increasing, and when is it decreasing?
x¢(t) = 3t 2 -18t + 24 = 3(t 2 - 6t + 8) = 3(t - 4)(t - 2)
So, x(t) has horizontal tangent lines when t=4 and t=2 sec.
x’(t)
+
0
0 +
<-------------------|----------------|-------------------->
2
4
x(t) = t3 – 9t2 + 24t
b) When is v increasing, and when is it decreasing?
c) When is the speed of the body increasing?
2. If x(t) = ½ t 4 – 5t 3 + 12t 2, find the velocity of the moving
object when its acceleration is zero.
Free Fall of an object:
1 2
y ( t ) = - gt + v 0 t + y 0
2
where g is the gravitational constant (32 feet per second per second,
or 9.8 meters per second per second).
So… in feet …
y ( t ) = -16t 2 + v 0 t + y 0
and in meters….
y ( t ) = -4.9t 2 + v 0 t + y 0
3. An object is dropped from a height of 20 feet. If we neglect air
friction, how long will it take for the object to hit the ground?
Give the velocity of the object on impact.
4. Supplies are dropped from a stationary helicopter and seconds
later hit the ground at 98 meters per second. How high was the
helicopter?
5. A stone, projected upward with an initial velocity of 112 ft/sec,
moves according to x(t) = – 16t2+112t, where x is the distance from
the starting point.
a) Compute the velocity and acceleration when t = 3 and
when t = 4.
b) Determine the greatest height the stone will reach.
c) Determine when the stone will have a height of 96 ft.
2. Suppose the position equation for a moving object is given by
x(t) = 3t2 + 2t + 5 where x is measured in meters and t is measured in
seconds. Find the velocity of the object when t = 2.
a) 13 m/sec
b) 14 m/sec
c) 10 m/sec
d) 6 m/sec
e) none of these
Some problems from the book:
dy
3. Find
: y  csc   cot 
d
4.
x2
Find the slope of the line normal to F  x  
at x = 1.
3x  1
5. An equation of the line tangent to the graph of y = cos(2x) at
x=

4
is?
1 2
6. At what point on the graph of y  x is the tangent line parallel to the
2
line 2x – 4y = 3?
 
7. If f (x) = tan (2x), then f '   =
6
8. If f  x   x 2x  3 , then f '  x   ?
 
d
2
3
9.
cos x 
dx
ìï2x 3 - 3
10. Let f ( x ) = í
ïî3x - 4
true?
x £1
x >1
which of the following statements is