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