As it is always the case that correct answers without sufficient mathematical justification may not receive full credit, make sure that you show all your work. Please circle, draw a box around, highlight, or otherwise clearly indicate your final answer for each question. By signing your name above, you attest to the fact that the work you are presenting is wholly your own. This work is due in class as assigned by the instructor and noted in the course syllabus. Attach all work to this coversheet.
1. Determine the open intervals on which the graph of f(x) = x5 + 5x4 - 40x3 is concave upward or concave downward.
2. Find the points of inflection and discuss the concavity of the graph of the function f (x) = x√(9-x).
3. Sketch the graph of a function f having the following characteristics:
f (0) = f (2) = 0 f'(x) > 0 if x > 1
f'(x) < 0 if x < 1 f"(x) > 0
f'(1) = 0
4. Sketch the graph of the function f(x) = 2x2/x2 - 4 using extrema, intercepts, symmetry, and asymptotes.
5. Analyze and sketch the graph of the function f (x) = (x2+1)/(x2 -4) Label any intercepts, relative extrema, points of inflection, and asymptotes.
6. Use the graph of f', given to the right, to sketch a possible graph of f and a possible graph of f".
