22: A rectangle is to be constructed that has a height of x and a length of 30 – x2. Determine the value of x that maximizes the rectangle's area, and show that this value of x achieves the maximum (as opposed to the minimum or something else).

14- Determine the maximum/minimum value of the following and when it occurs. y=3x²-24x+5

Julie has tracked Bouncy Ball company profits for severalyears, and her analysis has determined that the function,P(x) = –3x3 + 138x2 + 588x + 600, can be used to determineprofits, in dollars, every year for x years after 1980. 1) Find the y–intercept for the profit function and give an interpretation. 2) Determine the end behavior of the profit function.a) What is the behavior at the left end? Is this behavior relevant tocompany profits? If so, what does it say about company profits asx → – ∞? b) What is the behavior at the right end? Is this behavior relevant tocompany profits? If so, what does it say about company profits asx → ∞? 3) We will use the Rational Zeros Theorem to determine possible rational zerosof P(x). First, factor out the common factor of -3. 4) Use synthetic division to find at least one rational zero of P(x). Chapter 5: Polynomial Functions 69Profitable Venture Page 2 of 25) Use the zero found in item 4) along with the quotient to completely factorP(x). 6) What are…

4) The cost of making x items is C(x)=15+2x. The cost p per item and the number made x are related by the equation p+x=25. Profit is then represented by px-C(x) [revenue minus cost].   a) Find profit as a function of x b) Find x that makes profit as large as possible c) Find p that makes profit maximum.