1. For the function f defined below, determine if f is increasing or decreasing at x=2 and determine the concavity at x=2. f(x) = x-1-x2
2. Suppose that the function f has the following characteristics:
f'(x) < 0 for 0 < x < 1
f'(1) = 0
f'(x) > 0 for 1 < x < 2
then
Question options:
f has a local minimum at x = 1.
f has a local maximum at x = 1.
f has neither a local maximum or a local minimum at x = 1.
there is not enough information to determine if x = 1 is a maximum or minimum.
3. Find the distance from the origin to the point on the line y=-2x+3 that is closest to the origin. Round your answer to two decimal places.
4. Suppose you need to build a box with no top from a square sheet of metal by cutting squares of equal size out of each corner and folding up the flaps to form the four sides of the box. Find the maximum possible voulme in cubic inches of such a box if the square sheet of metal is 120 inches on each side.