Quiz 4

Name:
Group members:

Section:

Total points: 8

Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = e^{4 x^{2} + 3 x}. \] $f'(x) = $
Let $g(z) = - 8 z^{3} - 4$.
1. Calculate the slope of the secant line from $z=-8$ to $z=-7$.
  
  Slope =
2. Calculate the slope of the secant line from $z=k$ to $z=c$.
  
  Slope =
3. For any function $f(z)$, what is the slope of the secant line from $z=k$ to $z=c$?
  
  Slope =
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:
Compute the derivative, $\diff{f}{x}$, of the function $f(x)$ below \[ f(x) = 5 x^{3} + x^{2} + 5 x + 1. \] $f'(x) = $

Need help?Hide help

Hint
the hint
Hide help
Compute the derivative, $\diff{f}{x}$, of the function $f(x)$ below \[ f(x) = \left(3 x^{2} - 5 x + 2\right) e^{x}. \] $f'(x) = $
Given the function \[ g( x ) = \ln{\left (x^{2} - 14 x + 48 \right )}, \] calculate the slope of the tangent line at the point $x=3$.

tangent line slope =

Do not round or approximate your answer.