Question 1 (Essay Worth 10 points) (04.02) 9 Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 9x1'3 +x"3. You must justify your answer using an analysis of f '(x) and f "(x). Question 2 (Essay Worth 10 points) 1:3 (04.03) 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 nal answer' Question 3 (Essay Wonh 10 points) (04.04) The position function of a particle in rectilinear motion is given by s(t) = t3 12!2 + 45t + 4 for t 2 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. [E23 Question 4 (Essay Worth 10 points) (04.05) A circle is growing so that the radius is increasing at the rate of 5 cm/min. How fast is the area of the circle changing at the instant the radius is 20 cm? Include units in your answer.Question 5 (Essay Worth 10 points) (04.07) The side of a square is measured to be 16 ft with a possible error of 10.1 ft. Use linear approximation or differentials to estimate the error in the calculated area. Include units in your