Math 115
Section 003
Team Homework #5
Meghan, Kaydee, Ashley
Due 101608
3.1 #56
In this problem, we are given the equation y=x
2
2x+4.
We know that this is a parabola.
We know it opens up because the leading coefficient is positive.
We also know its vertex
is at (1,3).
The problem asks us to find the equations of all lines through the origin, and
tangent to the parabola.
The general equation of a line is y=mx+b.
Since the line must pass through (0,0), the y
intercept is at 0, and there will be no b.
The derivative of the equation is y’=2x2. We
also know that x
2
2x+4 = 2x
2
2x,
x
2 =
4,
x=+2
We substitute 2 and 2 in for the derivative:
2(2)2 = 2
and
2(2)2 = 6
Since these are the derivative, 2 and 6 are the values of the slope (m).
So, we now have to equations: y = 2x and y = 6
These two lines pass through the origin and are tangent to the parabola y = x
2
2x+4.
3.2 # 40
The problem tells us that V(t) = 25(0.85)
t
is the value of a certain automobile purchased
in1997.
V is the value, in thousands of dollars, and t is the time, in years, from the date
of purchase.
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 Fall '08
 BLAKELOCK
 Math, Calculus, Car, Automobile

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