QuestionMath
A manufacturer of lighting fixtures has daily production costs of where is the total cost (in dollars) and is the number of units produced. How many fixtures should be produced each day to yield a minimum cost?(Round your answer to two decimal places.)
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Math
1. For the function below, find the intervals of increase and decrease, and the intervals of concavity.
y = x3 +2×2 – 4x + 1
2. Determine the absolute and local extreme values of each function on the given interval.
a) f (x) = 2×3 – 3×2 – 12x + 2, – 3 x 3
b) f (x) = x3 + x , 0 x 10

3. Determine the angle between these two vectors below.
= [–6, 3, 0] and = [7, 2, 4]
4. Write the parametric equations of a line perpendicular to 4x + 8y + 7=0
with the same x-intercept as [x, y] = [2, 7] + t [–10, 3].

5. A plane is defined by the equation x – 4y + 2z – 16 = 0.
a) Find two vectors parallel to the plane.
b) Write the vector and parametric equations of the plane.

6. A certain computer that is purchased today depreciates in value according to the function V(t) = 900 e , V represents value, in dollars; t represents time, in years,
a) What was the purchase price of the computer?
b) What is its value after 1 year?
c) How long will it take for the computer’s value to decrease to half of its original value?
7. If = [5, 8, 2] , = [–7, 3, 6] , determine × and •
8. Determine the equation for the tangent line to the functions. a) y = 2×2 – 1 at x = – 2
b) y = 2sinx + 4cosx at x =
c) y = –3ex at x = ln3

Math
1. For the function below, find the intervals of increase and decrease, and the intervals of concavity.
y = x3 +2×2 – 4x + 1
2. Determine the absolute and local extreme values of each function on the given interval.
a) f (x) = 2×3 – 3×2 – 12x + 2, – 3 x 3
b) f (x) = x3 + x , 0 x 10

3. Determine the angle between these two vectors below.
= [–6, 3, 0] and = [7, 2, 4]
4. Write the parametric equations of a line perpendicular to 4x + 8y + 7=0
with the same x-intercept as [x, y] = [2, 7] + t [–10, 3].

5. A plane is defined by the equation x – 4y + 2z – 16 = 0.
a) Find two vectors parallel to the plane.
b) Write the vector and parametric equations of the plane.

6. A certain computer that is purchased today depreciates in value according to the function V(t) = 900 e , V represents value, in dollars; t represents time, in years,
a) What was the purchase price of the computer?
b) What is its value after 1 year?
c) How long will it take for the computer’s value to decrease to half of its original value?
7. If = [5, 8, 2] , = [–7, 3, 6] , determine × and •
8. Determine the equation for the tangent line to the functions. a) y = 2×2 – 1 at x = – 2
b) y = 2sinx + 4cosx at x =
c) y = –3ex at x = ln3