This preview shows page 1. Sign up to view the full content.
16A Practice Midterm II
1.Find the derivative of the following functions. DO NOT simplify your answers.
a)
f
(
x
)
=
12
x
4
!
7
x
3
+
b)
g
(
x
)
=
3tan
x
2
x
!
9
+
x
1/5
sec
x
c)
h
(
x
)
=
(3
x
3
+
2
x
)
7
+
9
x
2.
Find equations of the lines that are tangent to the graph of the function
f
(
x
)
=
x
3
!
6
x
+
5
and parallel to the line 3x + y + 4 = 0. Write your answers in slopeintercept form.
3.
Use implicit differentiation to find
dy
dx
for the curve
xy
=
y
2
+
x
3
!
1.
4.
Find all points on the graph of f(x) = cosx – sinx at which the tangent line is horizontal for
0
≤
x < 2
π
.
5.
Use the limit definition of the derivative to prove that
d
dx
[
cf
(
x
)]
=
c
d
dx
[
f
(
x
)]
6.
The height (in feet) of a toy rocket above the ground after t seconds is given by
s
(
t
)
=
!
16
t
2
+
96
t
+
288.
a)
What are the initial height and initial velocity of the rocket?
b)
Find the maximum height of the rocket.
c)
If the rocket hits the ground after 9 seconds, find intervals at which the speed is increasing.
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 06/23/2010 for the course MATH math16 taught by Professor Na during the Spring '10 term at UC Riverside.
 Spring '10
 NA
 Equations, Derivative

Click to edit the document details