MATH 203 Spring 2007

TEST 2

8 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. Compute the derivative of $f(x)=\ln (3x+2).$
    MATH

  2. Find all asymptotes of MATH and plot the graph of the function.
    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: $f(1)=1,$ and $f$ is increasing on $(-\infty ,0)$ and decreasing on $(0,\infty ),$ concave down on $(-1,1),$ up elsewhere, and $y=-1$ is a horizontal asymptote.
    MATH

  5. The graph of $f$ is given below. Completely describe the behavior of the function by using such words as "increasing/decreasing", "concave up/down", "max/min", "asymptotes", etc.
    MATH

    MATH

  6. The graph of $f$ is given below. For what values of $x$ are MATH positive, negative or zero? Fill in the blanks.
    MATH
    MATH

  7. Find absolute (global) maxima and minima of the function, $f(x)=x^{3}-3x$ on the interval $[-2,10].$
    MATH

  8. Set up, but do not solve, an optimization problem for the following situation: "If an open box is to be made from a tin sheet 8 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made."

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