Questions 7 and 8 pertain to the equation y = (2x 3)(x 1). (4.2.8)
7. a. Find dy/dx. _
(x)(4x 2x 3) / x
b. Find the equation of the line tangent to the curve at x = 4. _
(2x 3)(1 / x) + (x 1)(2)
(4x 2
Questions 1 through 3 pertain to the following situation. A projectile is shot straight up with an initial
velocity of 512 feet per second. Its height above the ground after t seconds is given by s(t)
Questions 13 and 14 pertain to the equation y = -6ex.
13. a. Find dy/dx. _ dy/dx = -6ex
b. Find the equation of the tangent line to the graph at the point on the graph where x = 0.
_ y = -6x 6
y(0) =
Questions 9 and 10 pertain to the equation y = (7)3x + 1
9. a. Find dy/dx. _ dy/dx = (7)(ln 3)(3x+1)
b. Find the equation of the tangent line to the graph at the point on the graph where x = -1.
_ y =
Questions 1 and 2 pertain to the following situation. If a rock is dropped from a 144-foot building, its
position (in feet above the ground) is given by s(t) = -16t 2 + 144, where t is the time in sec
9a. Find dy/dx. _ 10 / (x + 4)2
b. Find the equation of the tangent line to the graph of at x = 6. _ y = (1/10)x 7/5
[(x + 4)(3) (3x + 2)(1)] / (x + 4)2
y 2 = (1/10)(x 6)
2
[(3x + 12) (3x + 2)] / (x +
For questions 13 and 14, assume that a demand equation is given by q = 5000 100p, where p is the price
and q is the quantity sold at that price.
13. a. Express the demand equation with price as a func
Questions 19 and 20 pertain to the equation y = -(8x + 1).
19. a. Find dy/dx. _ 10 / (x + 4)2
b. Find the equation of the tangent line to the graph of at x = 3. _ y = (1/10)x 7/5
[(x + 4)(3) (3x + 2)(
Questions 5 and 6 pertain to the equation y = (x 1)3(x 3)2.
5. a. Find dy/dx. _ 2(x2 1)2(x 3)(4x2 9x 1)
b. Find the equation of the tangent line to the graph at the point on the graph where x = 2.
_ y
5. a. Find dy/dx. _ 2x2(x3 + 7)-1/3
b. Find the equation of the line tangent to this curve at x = 1. _ y = x + 3
y = u2/3 and u = (x3 + 7)
2(1)2(13 + 7)-1/3
when x = 1, y = 4
-1/3
2
-1/3
dy/du = (2/3)
Questions 1 and 2 pertain to the equation y = 4x2 x + 4.
1. a. Find dy/dx. _ 8x 1
b. Find the equation of the tangent line to the graph at the point on the graph where x = 0.
_ y = -31x + 24
if x = 0,
Commutative
Property
Of Addition
Identity Property of
Addition
Identity Property of
Multiplication
3+4=4+3
5+0=5
7x1=7
2x3=3x2
Commutative
Property of
Multiplication
Array
3x2
or 3 groups of 2
What un