1. (15 points) Let f (.12) = 1'3 12.1:2 + 363: 6. Find the intervals of increase/ decrease, any local extrema. the intervals of concavity, and any points of inflection. 2. (10 points) Find and classify all local extrema (as either local maxima or minima): f(:.'r:) E 1'4 - 83:2 + 2. 3. (10 points) Find f(:t) if f\"'(a:) : 30 + CBS 33! f(0) = 0, f'(0)- Err4, and f\"(0) ; 1L 4. (15 points) The top and bottom margins of a poster are each 8 cm and the side margins are each 6 cm. If the printed area should measure 900 square centimeters, nd the poster with the smallest possible area. [Suggestiom let :3 and y "be the horizontal and vertical dimensions (respectiveiy) of the printed area.) 5. (15 points) A stone was dropped from the top of a cliff, and hit the ground with a speed of 88 feet per second. How high is the clif? (Assume g = 32 feet per second squared.) 2 6. (15 points) Evaluate the integral / (llmg) do; using the limit denition (i.e., Riemann 2 sums). Also: CHECK YOUR AN WER using the fundamental theorem of calculus. [Note that 11 i 1 = 71' Xi = \"inf 1,. if: _ 11(nji1)'(2n 411) 7 T, S __. i=1 i=1 7. (20 points) Evaluate the following