AP Calculus Quiz Review 4.4-4.6
Name_
1. What is the largest possible area for a right triangle whose hypotenuse is 5 cm
long, and what are its dimensions.
2.
You are designing a rectangular poster to contain 50 in2 of printing with a 4-in
margin at the t
AP Calculus Exam Project Due by the end of the day on Thursday May 16
All late will receive a 10% deduction for each day past due date.
4
Explanation
Use of Visuals
Mechanics
Demonstrated
Knowledge
Requirements
Creativity
3
2
Complete lesson,
script, or p
DERIVATIVES - TRIG FUNCTIONS
1. f (x) = 4(cos x)
2. f (x) = 3x(sin x)
3. f (x) = x 3 (sin x)
4. f (x) = x ! x 2 (cos x)
5. f (x) =
sin x
x
7. f (x) = 2x(cos x) + x 2 (sin x)
9. f (x) = 3x 2 (sin x) ! x 3 (cos x)
6. f (x) =
x2
cos x
8. f (x) = sin x cot x
Implicit Differentiation
a) With respect to x
x 2 y + xy 2 = 6
dy
dy
dy 2
x + 2xy = 2xy y 2
1. 2x y + 1 x 2 + 1 y 2 + 2 y x = 0
dx
dx
dx
2
2xy y
dy
y(2x + y)
=
=
2
dx
x(x + 2 y)
x + 2xy
(
(
(
)
)
)
x 3 xy + y 3 = 1
dy
dy
dy
dy
= 0 3x 2 y x + 3y 2
=0
2.
DERIVATIVES - TRIG FUNCTIONS
1. f (x) = 4(cos x)
2. f (x) = 3x(sin x)
f '(x) = 3sin x + ( cos x ) 3x
f '(x) = 4 sin x
f '(x) = 3( sin x + x cos x )
3. f (x) = x 3 (sin x)
4. f (x) = x x 2 (cos x)
f '(x) = 3x 2 ( sin x ) + ( cos x ) x 3
f '(x) = 1 2x cos x