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(Step-by-Step) The length, L, height h, and width w of an open box (i.e., no top) change with time. At a certain instant the dimensions are L = 8 cm, w =

Question: The length, L, height h, and width w of an open box (i.e., no top) change with time. At a certain instant the dimensions are L = 8 cm, w = 5 cm, and h = 10 cm; L and w are increasing at a rate of 0.15 cm/sec, and h is decreasing at a rate of 0.40 cm/sec. At that instant, find the rate at which the surface area of the box is changing and the rate at which the volume is changing (include units with the rates). Is the surface area and volume increasing or decreasing at this instant? Please give reasons for your answers.

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