Quiz 4

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Total points: 8

Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \left(3 x^{2} + 5 x\right) \ln{\left (x \right )}. \] $f'(x) = $
Let $g(y) = - 2 y^{3} + 1$.
1. Calculate the slope of the secant line from $y=-1$ to $y=-9$.
  
  Slope =
2. Calculate the slope of the secant line from $y=k$ to $y=d$.
  
  Slope =
3. For any function $f(y)$, what is the slope of the secant line from $y=k$ to $y=d$?
  
  Slope =
Compute the derivative, $\diff{f}{x}$, of the function $f(x)$ below \[ f(x) = 5 x^{4} - 4 x^{3} - 4 x - 2. \] $f'(x) = $

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The blue curve is the graph of a function $g(x)$. (It is called a piecewise linear function, because it is composed of pieces of linear functions.) Move the magenta line segments up and down so that the magenta line segments form the graph of the derivative $g'(x)$.

Feedback from applet
Given the function \[ h( y ) = \ln{\left (y^{2} + 7 y - 8 \right )}, \] calculate the slope of the tangent line at the point $y=-4$.

tangent line slope =

Do not round or approximate your answer.
Compute the derivative, $\frac{df}{dx}$, of the function $f(x)$ below \[ f(x) = \ln{\left (4 x^{2} - 4 x + 1 \right )}. \]
$f'(x) = $