Answer each question with showing your work.

*" Note: For these questions. all answers must be determined algebraically. That is, HGT determined by analyzing a graph of the function. You can graph the function to check your results, but an algebraic analysis, using the techniques covered in the lessons, must be shown. 1. Determine the intervals on which the curve is concave upward or concave downward and state the points of inflection forgi-Ir = x\" 241:2 + x l 2. Given f(x) = x4 - 8x2 , use the curve sketch algorithm to determine: The it 3: y intercepts The intervals of increase or decrease The local maximum and minimum values The intervals of concavity The points of inflection Sketch the curve using the grid below, or on an axis that is created using a ruler and proper scale. irt-1ft!!!" 1. Find two numbers whose difference is 150 and whose product is a minimum. 2. A box with an open top is to be constructed from a square piece of cardboard, 3m wide, by cutting out a square of length x from each of the four corners and bending up the sides, as indicated in the figure. Determine the largest volume that such a box can have