5. Let A be the area of a square whose sides have length x, and assume that x varies with the time t. (a) Draw a picture of the square with the labels A and x placed appropriately. (b) Write an equation that relates A and x. (c) Use the equation in part (b) to find an equation that relates dA/dt and dx/dt. (d) At a certain instant the sides are 3 ft long and increasing at a rate of 2 ft/min. How fast is the area increasing at that instant?
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- Draw a square and label each side as \( x \) (since each side of the square has the same length). - Label the area inside the square as \( A \). Show more…
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