Calculus Section 4.5 Solve max/min problems Recall: The max/min value of a function occurs at a point where the derivative of the function is either zero.

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Presentation transcript:

Calculus Section 4.5 Solve max/min problems Recall: The max/min value of a function occurs at a point where the derivative of the function is either zero or undefined. To find the max/min value of a function 1.Write a function for the quantity that is to be maximized or minimized. 2.Find the derivative of the function and determine the critical numbers. 3.Determine whether the critical numbers are a max or min value.

A manufacturer of telephones determines that the profit from producing and selling x telephones is P(x) = -.01x 2 + 6x – 500 dollars. a. How many telephones should be produced to maximize the profit? b. What is the maximum profit?

A rocket is launched vertically such that its distance s (ft) from the ground at any time t (seconds) is given by s(t) = -16t t. How high will the rocket travel before falling back to the ground?

A family plans to fence in a rectangular patio area behind their house. They have 120 feet of fence to use. What dimensions would make the rectangular area as large as possible?

A manufacturer can sell x headphones at a price of x dollars each. It costs 40x + 15,000 dollars to produce all x of them. How many headphones should be produced to maximize profit?

A manufacturer of storage bins plans to produce some open top rectangular boxes with square bases. The volume of each box is to be 100 cubic ft. Material for the base costs $8 per square ft, and the material for the sides cost $5 per square ft. Determine the dimensions of the box that will minimize the cost of the materials.

assignment Page 231 Problems 2 – 40 even