Math Insight

Quiz 4

Name:
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Section:
Total points: 8
  1. 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:

  2. Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \left(6 x^{2} + 4 x\right) \ln{\left (x \right )}. \] $f'(x) = $

  3. Compute the derivative, $\diff{f}{x}$, of the function $f(x)$ below \[ f(x) = x^{4} - 2 x^{3} - 4 x^{2} + 7 x - 14. \] $f'(x) = $

  4. Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \ln{\left (5 x^{2} - 4 x - 5 \right )}. \]
    $f'(x) = $

  5. Let $g(z) = - 2 z^{3} + 3$.

    1. Calculate the slope of the secant line from $z=-10$ to $z=0$.

      Slope =

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

      Slope =

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

      Slope =

  6. Given the function \[ g( t ) = e^{t^{3} - 52 t + 96}, \] calculate the slope of the tangent line at the point $t=2$.

    tangent line slope =

    Do not round or approximate your answer.