Question

# 1.

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) =

3x(1/3) + 6x(4/3). You must justify your answer using an analysis of f ‘(x) and f (x). (10 points)

2.

What is the maximum volume in cubic inches of an open box to be made from a 16-inch by 30-inch piece of cardboard by cutting out squares of equal sides from the four corners and bending up the sides? Your work must include a statement of the function and its derivative. Give one decimal place in your final answer. (10 points)

3.

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0 with t measured in seconds and s(t) measured in feet. Find the position and acceleration of the particle at the instant when the particle reverses direction. Include units in your answer. (10 points)

Math