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5.4

Optimization. 5.4. A Classic Problem. You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What is the maximum area that you can enclose?. 1 Write it in terms of one variable. 2 Find the first derivative and set it equal to zero.

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5.4

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  1. Optimization 5.4

  2. A Classic Problem You have 40 feet of fence to enclose a rectangular garden along the side of a barn. What is the maximum area that you can enclose?

  3. 1 Write it in terms of one variable. 2 Find the first derivative and set it equal to zero. 3 Check the end points if necessary. To find the maximum (or minimum) value of a function:

  4. An open-top box is to be made by cutting congruent squares of side length x from the corners of a 20- by 25-inch sheet of tin and bending up the sides. How large should the squares be to make the box hold as much as possible? What is the resulting maximum volume? Verify that this is a max. Check the endpoints.

  5. Homework pg 281 #1-3,7,8,18 Calculator on #18. pg 281 #4,5, 10-13,16

  6. Find two numbers whose sum is 40 and whose product is as large as possible. What is the smallest perimeter possible for a rectangle whose area is 25 square inches?

  7. Find the point on the curve that is closest to the point (18,0).

  8. Inscribing Rectangles A rectangle has its base on the x-axis and its upper two vertices on the parabola . What is the largest area the rectangle can have, and what are its dimensions?

  9. What dimensions for a one liter cylindrical can will use the least amount of material? Motor Oil We can minimize the material by minimizing the area. We need another equation that relates r and h: area of ends lateral area

  10. What dimensions for a one liter cylindrical can will use the least amount of material? area of ends lateral area

  11. Homework pg 281 #1-3,7,8,18 Calculator on #18. pg 281 #4,5, 10-13,16

  12. Find the maximum distance, measured vertically, between the graphs of

  13. Inscribing Rectangles A rectangle has its base on the x-axis and its upper two vertices on the parabola . What is the largest area the rectangle can have, and what are its dimensions?

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