Calculus

1).Find the absolute maximum and minimum values of the function over the indicated interval, and indicate the x-values at which they occur.

F(x)=4+3x-3x^2; [0,2]

The absolute maximum value is __ at x=____

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

2. 3x^3-3x^2-3x+5; [-1,2]

The absolute maximum value is __ at x=____

3. f(x)= x^3-9x^2; [0,13]

(Use a comma to separate answers as needed.)

4. f(x)= x^3-12x; [-6,2]

The absolute maximum value is __ at x=____

5. f(x)= 4+6x^3; [-5,5]

The absolute maximum value is __ at x=____

6. f(x)=15x^4-4x^3, [-2,2]

The absolute maximum value is __ at x=____

7. f(x)= 3x/x^2+4; [-7,7]

(the 3x is completely over the x^2+4)

The absolute maximum value is __ at x=____

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

8. Find the absolute maximum and minimum values of the function, if they exist, over the indicated interval. Also indicate the x-value at which each extremum occurs.

F(x)=4x+4/x; (0,infinite)

(4x plus 4 over the x)

9. Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue, R(x), and cost, C(x), of producing x units are in dollars

R(x)=60x-0.5x^2, C(x)=6x+15

In order to yield the maximum profit of $__, __ units must be produced and sold.

(Simplify your answers. Round to the nearest cent as needed.)

10. R(x)=6x, C(x)=0.01x^2+0.3x+4

What is the production level for the maximum profit? ___units

Therefore, the maximum profit of ___ occurs at a production of ___ units.

11. Find the maximum profit and the number of units that must be produced and sold in order to yield the maximum profit. Assume that revenue,

R(x)=9x-3x^2, C(x)=x^3-5x^2+2x+1

The production level for the maximum profit is about__ units

(Do not round until the final answer. Then round to the whole number as needed.)

Therefore, the maximum profit of ___ occurs at a production of about ___units.

12. A university is trying to determine what price to charge for tickets to football games. At a price of $16 per ticket, attendance averages 40,000 people per game. Every decrease of $4 adds 10,000 people to the average number. Every person at the game spends an average of $6.00 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?

What is the price per ticket?

Therefore, the revenue is maximized when the price per ticket is ___. At that price, the average attendance will be ____ people.

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