Math 151 practices

  1. If the graph of $f$ is given below: MATH

    1. Compare MATH in increasing order.

    2. Find the interval(s) where $f^{\prime }$is positive.

    3. Find the interval(s) where $f^{\prime }$is negative.

  2. If the graph of $f^{\prime }$ (derivative of a function) is given below: MATH

    1. Compare MATH in increasing order.

    2. Indicate the '$x-value^{\prime }$ where $f$ has relative maxima.

    3. Indicate the MATH where $f$ has relative minimum.

  3. Given the position funtions for two race cars $f$ (thin) and $g$ (thick) are shown as follows and suppose the graphs of $y=f(x)$ and $y=g(x)$ intersect at $x=1.8.$ Then answer the following questions:MATH

    1. Do these two cars start at the same position?

    2. Which car starts out faster?

    3. Where do these two cars meet?

    4. Compare $f^{\prime }(x)$ and $g^{\prime }(x)$ for $x\geq 1.8.$

  4. Label the graphs for $f,f^{\prime }$ and $f^{\prime \prime }$
    graphics/test3__27.png

  5. If the graphs of MATH and MATH are given below: Then

    1. identify the graph for MATH and MATH respectively.

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

    3. find the maximum and minimum for $f$ in the interval $[0,2\pi ],$

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

      MATH

  6. Find the following limits:

    1. MATH

    2. MATH

    3. MATH

    4. MATH

    5. MATH

  7. Find two functions which are continuous everywhere but are not differentiable everywhere.

  8. Use the definition for the derivative function, MATH to find $f$ and $a$ from the expression MATH

  9. Use the definition for the derivative function, MATH to find $f^{\prime }(a)$ if $f(x)=x^{2}+2x.$