g(x)=10/(10+3x^2)

horizontal asymptote y=

vertical asymptote x=

g(t)= (t+3)/(7t-3)

horizontal asymptote g=

vertical asymptote t=

g(x)=10x^3+x^2+5

horizontal asymptote g=

vertical asymptote x=

g(x)= x^3/(x^2-81)

horizontal asymptote y=

vertical asymptote x=

vertical asymptote x=

f(x)=2x/(x^2-2x-15)

horizontal asymptote y=

vertical asymptote x=

vertical asymptote x=

h(x)=(2-x^2)/x^2+2x

horizontal asymptote y=

vertical asymptote x=

vertical asymptote x=

Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.)

f(x)=-x^2+4x+7

max=

min=

f(x)=x/(16+x^2)

max=

min=

f(x)=x^2-x-3 on (0,3)

max=

min=

f(x)=x^3+3x^2+8 on (-3,2)

max=

min=

f(x)=t/(t-10) on 912,14)

max=

min=

f(x)=10x-10/x on (5,7)

max=

min=

Lynbrook West, an apartment complex, has 100 two-bedroom units. The monthly profit (in dollars) realized from renting out x apartments is given by the following function.

P(x)=-12x^2+2160x-50000

To maximize the monthly rental profit, how many units should be rented out?_____units

What is the maximum monthly profit realizable

The quantity demanded each month of the Walter Serkin recording of Beethoven's Moonlight Sonata, manufactured by Phonola Record Industries, is related to the price per compact disc. The equation

p=-0.00049x+6 ( 0<=x<=12000)

where p denotes the unit price in dollars and x is the number of discs demanded, relates the demand to the price. The total monthly cost (in dollars) for pressing and packaging x copies of this classical recording is given by

c(x)=600+2x-0.00001x^2 (0<=x<=20000)

To maximize its profits, how many copies should Phonola produce each month? Hint: The revenue is R(x) = px, and the profit is P(x) = R(x) - C(x). (Round your answer to the nearest whole number.)

________discs/month