Determine whether the equation defines y as a linear function of x. If so, write it in the form y=m x+b.

Determine whether the equation defines $y$ as a linear function of $x$. If so, write it in the form $y=m x+b$.
$x=2 y-4$
Determine whether the given function is a polynomial function, a rational function, or some other function. State the degree of each polynomial function.
$f(x)=3 x^{6}-2 x^{2}+1$
A manufacturer has a monthly fixed cost of $\$ 40,000$ and a production cost of $\$ 8$ for each unit produced. The product sells for $\$ 12$ /unit.

What is the cost function?
What is the revenue function?
What is the profit function?
Compute the profit (loss) corresponding to production levels of 8000 and 12,000 units.

4. EFFECT OF ADVERTISING ON SALES. The quarterly profit of Cunningham Realty depends on the amount of money $x$ spent on advertising/quarter according to the rule

$P(x)=-\frac{1}{8} x^{2}+7 x+30 \quad(0 \leq x \leq 50)$

.where $P(x)$ and $x$ are measured in thousands of dollars. What is Cunningham's profit when its quarterly advertising budget is $\$ 28,000$ ?

5. Find the derivative of $f\left( x \right)=3$ .

6. Find the derivative of $f\left( x \right)=3{{x}^{2}}$

7. Find the derivative of $f(x)=3 \sqrt{x}$

8. Find the derivative of $f(x)=5 x^{2}-3 x+7$

9. Find the derivative of $f\left( x \right)=\frac{{{x}^{3}}-4{{x}^{2}}+3}{x}$

10. Find the derivative of $f(x)=4 x^{4}-3 x^{5 / 2}+2$

11. Find the derivative of $f(t)=\frac{4}{t^{4}}-\frac{3}{t^{3}}+\frac{2}{t}$

12. Find the derivative of $f(x)=2 x-5 \sqrt{x}$

13. In Exercises 41-44, find the slope and an equation of the tangent line to the graph of the function $f$ at the specified point.

$f(x)=2 x^{2}-3 x+4 ;(2,6)$