Chapter 3 Homework

1. Find the derivative of the function

$h\left(x\right) = x^2+\frac{2}{x}$

2.  Find the derivative of the function

$f\left(x\right) = \frac{\sqrt{x}–1}{\sqrt{x}+1}$

3.  Find the derivative of the function

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

4. Find the derivative of the function

$f\left(x\right) =2x^4–3x^3+2x^2+x+4$

5.  Find

  by implicit differentiation

$y^3+3x^2=3y$

6.  Find

  by implicit differentiation

$x^2+2x^2{y}^2+y^2=10$

7.  Let

Find the points on the graph of f at which the slope of the tangent line is equal to -4

8. Find the equation of the tangent line to the graph of 

$y=x{(x+1)}^5 at the point (1,32)$

9  The number of subscribers to CNC Cable Television in the town of Randolph is approximated by the function  

where N(x) denotes the number of subscribers to the service in the xth week.

Find the rate of increase in the number of subscribers at the end of the 12th week.

10.  The marketing departments of Telecon has determined that the demand for their smart phones obeys the relationship

where p denotes the phone’s unit price (in dollars) and x denotes the quantity demanded.

(B) Find the Marginal Revenue Function R’