Math Insight

Quiz 4

Name:
Group members:
Section:
Total points: 8

  1. Let $f(z) = - 3 z^{3} - 2$.

    1. Calculate the slope of the secant line from $z=7$ to $z=-4$.

      Slope =

    2. Calculate the slope of the secant line from $z=m$ to $z=c$.

      Slope =

    3. For any function $g(z)$, what is the slope of the secant line from $z=m$ to $z=c$?

      Slope =

  2. Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \ln{\left (4 x^{2} + 4 x - 3 \right )}. \]
    $f'(x) = $

  3. Compute the derivative, $\diff{f}{x}$, of the function $f(x)$ below \[ f(x) = \left(5 x^{2} + 2 x - 3\right) e^{x}. \] $f'(x) = $

  4. Given the function \[ h( z ) = \ln{\left (z^{2} - 7 z + 10 \right )}, \] calculate the slope of the tangent line at the point $z=3$.

    tangent line slope =

    Do not round or approximate your answer.

  5. The green parabola, below, is the graph of the quadratic function $f$. (Quadratic means $f(x)=ax^2+bx+c$ for some parameters $a$, $b$, and $c$.) Using the three blue points, manipulate the blue curve so that it is the graph of the derivative $f'(x)$ of $f(x)$.
    Feedback from applet
    derivative:
    zero points:

  6. Compute the derivative, $\diff{f}{x}$, of the function $f(x)$ below \[ f(x) = x^{3} + 4 x^{2} + 8. \] $f'(x) = $
    Need help?

Thread navigation

Math 201, Spring 19