Quiz 1 Math 152 Print Name: Time

  1. Find the largest area of a rectangle in the first quadrant under the curve $y=\sqrt{4-x^{2}}.$


    Figure

    Figure

    The thin is original, and the thick is derivative.
    Figure

  2. At $10$ am, the ship $A$ is $60$ miles north of the ship $B.$ We know that the ship $A$ is going eastward at $20$ miles per hour and the ship $B$ is going north at $16$ miles per hour.

    1. Set up the distance function between the ship $A$ and the ship $B$.

    2. Set up the rate of change of the distance (between $A$ and $B)$ with respect to time.

    3. When is the distance between the ship $A$ and the ship $B$ closest?

      ** See the screen above for setting up the distance function.
      Figure

  3. If $f(x)=x\sqrt{3-x},$ then

    1. find the critical numbers of $f,$

    2. find the interval(s) where $f$ is increasing or decreasing,

    3. find the relative maximum or relative minimum of $f,$


      Figure

      Figure

  4. If MATH

    1. find the critical numbers of $f,$

    2. find the interval(s) where $f$ is increasing or decreasing,

    3. find the relative maximum or relative minimum of $f,$

    4. find the interval(s) where $f$ is concave upward or concave downward,

    5. find the inflection point(s) of $f.$


      Figure

      Figure

      Figure