Power Mean Inequalities

Power Mean Inequalities Problem Solving


What is the minimum possible perimeter of a rectangle with area 25?

If x2+y2=1, x^2 + y^2 = 1, find the maximum value of (x+y)2. (x + y)^2.

Suppose that a company produces right-cylindrical soup cans with radius r r and h h . If the volume is constrained to be a fixed value, which of the following dimensions minimizes the material per can?

Suppose g(x) g(x) is positive for all x x . Determine the minimum value of

f(x)=16(g(x))2+1g(x). f(x) = \frac{16 (g(x))^2 + 1}{g(x)}.

What is the minimum possible surface area of an open box (that is, a rectangular prism without its top) whose volume is 108 108 ? (Count only the exterior surface area.)


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