# Math Insight

### Quiz 4

Name:
Group members:
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. 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 =

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

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

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

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 =