Exam 2

1.  True or False

The derivative of

2.  Multiple Choice

Find the derivative of

3.  Multiple Choice

Find the derivative of the function

$f\left(x\right)=(x+1)(x–8)$

4.  Multiple Choice

Find the derivative of the function 

$f\left(x\right)=\frac{x–5}{2x}$

5   Multiple Choice

Find the derivative of the function

$f\left(x\right)={(2x^3+1)}^{3.1}$

6.  True or False

The second derivative of the function

$f\left(x\right)={(4x+1)}^{–\frac{1}{3}}$

is

$f‘‘\left(x\right)=\frac{–4}{3}{(4x+1)}^{\frac{–4}{3}}$

7.  File Upload

A toy company sells kids’ toys, the total cost of producing x is given by the function 

$C\left(x\right)=2350+80x–0.03x^2$

Find the marginal cost of producing the 5th unit.  No rounding.

8. Find the derivative with respect to t,  dx / dt

$x^{2}y=12$

9.   The volume of a cone of radius r and height h is given by the equation 

$V=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

If the radius increases at a constant rate of 0.5 cm/s and 

the height increases at a constant rate of 0.25 cm/s at what rate in  

is the volume increasing when the height is 12 cm and the radius is 8 cm?

10. True or False

Given the graph below

$\left[–4,–3\right]\cup \left[1,5\right]\cup \left[8,12\right]$

is the interval where the function is decreasing.

11.  Multiple Choice

Given the graph below state the interval where the function is concave upward

12. True or False

Given the graph below the vertical asymptote is y = 1

13  

Multiple Choice

Given the function determine all horizontal asymptotes

$f\left(x\right)=\frac{2x^2+x–6}{2x^2–x–3}$

14.    Multiple Choice

The game console manufacturer determines to sell x units at the price 

,  where p is in dollars.  

The manufacturer also determine that the cost depends on the fixed cost $100,000

and a variable cost 100 x, that is  

What price per unit must be charged to get the minimum profit?

  To get the minimum profit you should charge $300 per unit 
  To get the minimum profit you should charge $2000 per unit 
  To get the minimum profit you should charge $2300 per unit 
   None of the Above