11. DETAILS LARCALC11 13.10.027. Use Lagrange multipliers to find the minimum distance from the curve or surface to the indicated point. Point (3,1,1) Surface Plane: x+y+z=1
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- How are the absolute maximum and minimum similar to and different from the local extrema?Let P = (x,y) be a point on the graph of y = x2 - 3. d(x) = sqrt x4-5x2+9 Use a graphing utility (TI-84+) to graph d = d(x) in order to answer the following question For what positive value of x is d smallest? What do I enter into my calculator in order to find the correct minimum? In other words, what equation do I enter in so that I can get the proper minimum value?find the point on the line y=2x+10 that is closest to the orgin, (0,0) What is the minimum distance?
- A company is manufacturing a trash can with a volume of 4 cubic ft that has a cylindrical body and a hemispherical lid (illustrated below). If the hemispherical lid is to be made of a material costing $2.50 per square ft and the cylindrical body and circular base are to be made of a material costing $2 per square ft, determine the radius r and the height h of the cylindrical body that will minimize the cost of manufacturing the trash can. Then find the minimum cost of the trash can. Hint: You will need the surface area and volume formulas for a cylinder and a sphere. must show all stepsA worker is to construct an open rectangular box with a square base and a volume of 147 ft3. If material for the bottom costs $6/ft2 and material for the sides costs $7/ft2 what dimensions will result in the least expensive box? What is the minimum cost? Let x be the length of one side of the base of the box. Express the total cost of the materials, C, in terms of x. Find C(x)If a rectangle has its base on the x-axis and two vertices on the curve y=e^-x^2, show that the rectangle has the largest possible area when the two vertices are at the points of inflection of the curve.