Suppose you are buying a rectangular piece of carpet with perimeter 20 m. It's sides are...

 

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Suppose you are buying a rectangular piece of carpet with perimeter 20 m. It's sides are length xm and (10x) m for some x. What is the maximum possible area of the carpet? Does this answer change if you are told that each side has length at least 3 m? Question A3: Suppose f(x) is a differentiable function on the interval (a, b), with g(x) = f'(x). (a) Is it true that if (c, f(c)) is a point of inflection for some c = (a, b), then c is a critical point for g? (b) Is it true that if c = (a, b) is a critical point for g then (c, f(c)) is a point of inflection of f? Suppose you are buying a rectangular piece of carpet with perimeter 20 m. It's sides are length xm and (10x) m for some x. What is the maximum possible area of the carpet? Does this answer change if you are told that each side has length at least 3 m? Question A3: Suppose f(x) is a differentiable function on the interval (a, b), with g(x) = f'(x). (a) Is it true that if (c, f(c)) is a point of inflection for some c = (a, b), then c is a critical point for g? (b) Is it true that if c = (a, b) is a critical point for g then (c, f(c)) is a point of inflection of f?