MATH 203 Spring 2009

TEST 2

7 problems, 10 points each

Instructions:

1. Show enough work to justify your answers

2. Write the problems in the given order.

3. Start each problem on a new page.

4. Don't leave blank pages.

  1. Find the intervals on which the function $f(x)=xe^{x}$ is concave up and concave down.
    MATH

  2. Find all asymptotes of MATH.
    MATH

  3. The graph of function $f$ is given below. Sketch the graph of the derivative $f^{\prime }(x)$ in the space under the graph of $f$.
    MATH

  4. Sketch the graph of a function with the following properties: $f(0)=0,$ $f\nearrow $ on $(-2,1),$ $f\searrow $ $\ $on $(1,3),$ concave up on $(-2,0),$ up elsewhere, and $x=3$ is a vertical asymptote.
    MATH

  5. The graph of $f$ is given below. Describe the behavior of the function using: "increasing/decreasing on interval", "concave up/down on interval", "max/min at", "asymptotes are", etc.
    MATH

    MATH

  6. The altitude (in feet) attained by a model rocket $t$ seconds into the flight is given by the function:
    MATH
    Find the maximum altitude attained by the rocket.
    MATH

  7. Set up, but do not solve, an optimization problem for the following situation: "200 yards of fencing is available to construct a rectangular enclosure. What are the dimensions of the enclosure with the largest area if you build it adjacent to a river (3 sides)?"

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