The daily cost of producing $x$ high performance wheels for racing is given by the

following function, where no more than $100$ wheels can be produced each day.

$C|x=(x^4-1{)}^{\frac{1}{2}}$;xin$[1,100]$

The sailing prise for the wheel is $205$$$.$

a$)$ Find Revenue $R(x)$

b$)$ Find marginal Revenue

c$)$ Find Marginal Cost. Explain result in a simple language.

d$)$ Find average Cost

e$)$ Find Average marginal Cost. Explain result in a simple

language.

f$)$ Find Profit function, $P(x)$

g$)$ Find marginal Profit. Explain result in a simple language.

The profit function of a company XYZ is given by

$P(x)=2x^3-3x^2-12x+4,$

where $x$ is the number of years since $2000($i$.$e$.x=0$ correspond to the year $2000).$

a$)$ Find at which years the profit was biggest$/$smallest$.$

b$)$ State all the local and global extrema.

c$)$ Find point of the diminishing return for the Profit function.