Find all relative extrema of the function. use the second derivative test where applicable. (if an answer does not exist, enter
dne.) f(x) = x2 + 3x − 1
1 answer:
The given quadratic describes a parabola that opens upward. Its one absolute extreme is a minimum that is found at x = -3/2. The value of the function there is
(-3/2 +3)(-3/2) -1 = -13/4
The one relative extreme is a minimum at (-1.5, -3.25).
_____
For the parabola described by ax² +bx +c, the vertex (extreme) is found where
x = -b/(2a)
Here, that is x=-3/(2·1) = -3/2.
(-3/2 +3)(-3/2) -1 = -13/4
The one relative extreme is a minimum at (-1.5, -3.25).
_____
For the parabola described by ax² +bx +c, the vertex (extreme) is found where
x = -b/(2a)
Here, that is x=-3/(2·1) = -3/2.
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Answer:
66.42°
Step-by-step explanation:
<u>Given:</u>
A(5, 3t+2, 2)
B(1, 3t, 2)
C(1, 4t, 3)
BA • BC = 4
Step 1: Find t.
First we have to find vectors BA and BC. We do that by subtracting the coordinates of the initial point from the coordinates of the terminal point.
In vector BA B is the initial point and A is the terminal point.
BA = OA - OB = (5-1, 3t+2-3t, 2-2) = (4, 2, 0)
BC = OC - OB = (1-1, 4t-3t, 3-2) = (0, t, 1)
Now we can find t because we know that BA • BC = 4
BA • BC = 4
To find dot product we calculate the sum of the produts of the corresponding components.
BA • BC = (4)(0) + (2)(t) + (0)(1)
4 = (4)(0) + (2)(t) + (0)(1)
4 = 0 + 2t + 0
4 = 2t
2 = t
t = 2
Now we know that:
BA = (4, 2, 0)
BC = (0, 2, 1)
Step 2: Find the angle ∠ABC.
Dot product: a • b = |a| |b| cos(angle)
BA • BC = 4
|BA| |BC| cos(angle) = 4
To get magnitudes we square each compoment of the vector and sum them together. Then square root.
Rounded to two decimal places:
Answer:
The future value of this initial investment after the six year period is $2611.6552
Step-by-step explanation:
Consider the provided information.
A student desired to invest $1,540 into an investment at 9% compounded semiannually for 6 years.
Future value of an investment:
Where Fv is the future value, p is the present value, r is the rate and n is the number of compounding periods.
9% compounded semiannually for 6 years.
Therefore, the value of r is:
Number of periods are: 2 × 6 = 12
Now substitute the respective values in the above formula.
Hence, the future value of this initial investment after the six year period is $2611.6552