AP Calculus
K57 [WW/H
Test #4 Review: Di'erenliabiliw, Implicit, Related , Inverse Trig, MVT, Rolles
1) Indicate the locations where f(x) is 2) Indicate the locations on f(x) where a
not differentia
Name_ Block_ Due
Date_
AP Calculus
Limits, Continuity, IVT FRQ
*NO Calculator Allowed*
The function f is defined as .
a) Find .
b) Is f(x) guaranteed to have a root on the closed interval [-2, 3]? Jus
AP Calculus AB and BC
Summer Assignment 2014
This is your summer assignment. It covers topics learned in Algebra 2 and Math Analysis/Trig. These
are topics that are prerequisite to being successful in
2-5: Implicit Differentiation:
1.
Find using Implicit Differentiation.
2.
3.
4.
Find by implicit differentiation and evaluate the derivative at the given point or x-value.
5.
6. at x = -2
7. Find the
APCALCULUS,AB
20142015
Teaching Strategies
Students taking AP Calculus are expected to have a strong Algebra and PreCalculus foundation. As a
group we will work extensively on study habits, algebra sk
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SOLUTIONS T0 PRACTECE PROBLEM SET 4
54;:3 + 1 6x I
First, expand (4x2 + 1)2 to get 161'4 + 8x2 + 1 . Now, use the Power Rule to take the
derivative of each term. The derivative of 1 6x4 = 1 6(4)(3
ll.
12.
13.
14
15
16.
17.
' 18.
19.
23.
24.
25.
x(2x + 7)(x 2)
{QR/ENE)
ax5+bx4+cx3+dx2+ex+f
THE PRODUCT RULE
Now that you lqtow how to find. derivatives of simple polynomials, its time to get mo
Derivatives Review
1. Calculate
dy
for the following functions. Show the work that leads to your answers. Simplify
dx
Review all of the
derivative
completely. Factor out GCFs, no negative exponents, c
AP Calculus (AB) Motion Problems
1) A coin is dropped from a height of 64 ft. if 5 ft is the height ofthe stone t sec after being dropped,
then 5(1) = ~16t2 +64. (a) How long does it take the coin to
AP Calculus (AB)
Motion FRQ
1) On a recent visit to New York City, Mr. Texler was hit in the head with an egg from the top of the
Empire
State Building. This is another reason Mr. Texler doesnt like t
Name _ Date_
AP Calculus (AB)
Limits Test Review (Ch.1 & 3-5)
Please show work on separate paper.
1.
2.
5.
6.
9.
10.
13.
3.
7.
4.
8.
11.
12.
14.
16.
17. If , find
22.
15.
18.
23.
For what value of a d
AP Calculus (AB)
Motion Problems
1) A coin is dropped from a height of 64 ft. If s ft is the height of the stone t sec after being
dropped, then . (a) How long does it take the coin to reach the groun
Name_ Block_ Due
Date_
AP Calculus
Limits, Continuity, IVT FRQ
*NO Calculator Allowed*
The function f is defined as .
a) Find .
b) Is f(x) guaranteed to have a root on the closed interval [-2, 3]? Jus
Derivative Bingo
from John Handley High School
Name_
Directions: Find the first derivative of each function below. Locate the derivative on the Bingo card
below. Circle the answer. Keep working proble
Wit/la
,6?
PRODUCT RULE AND QUOHENT RULE 5 7
Differentiate. Use proper notation and simplify your nal answers.
In some cases it might be advantageous to simplify/rewrite rst.
Please work together Wit
TurveyforRelatedRates
In 1953, Roger Price invented a minor art form called the Droodle,
which he described as "a borkley-looking sort of drawing that doesn't
make any sense until you know the correct
Special Cases:
A)
B)
C)
y
y
y
x
x
x
D)
E)
Unbounded
Behavior
y
y
x
Oscillating Behavior
x
Practice:
1)
2)
8
y
7
6
8
5
7
4
y
6
3
5
2
4
1
3
2
8 7
6
5
4
3
2
1
1
1
2
3
4
5
6
7
8 x
1
2
8 7
3
6
5 4
3
2
1
1
Name
Date
._~-
_
Notes: 2-2 Particle Motion - Moving Along a Straight Line
I. Rules:
a.
When velocity is positive the particle is moving to the right.
b.
When velocity is negative the particle is movi
Please work together with
PRODUCTRULEANDQUOTIENTRULE classmates on this
your
assignment. Help
someone!
1. a) Find f ( x) for f ( x) =5 x sin x
2. a) Find f ( x) for f ( x) =(1 x )( x 3 )
b) Write the