calculus word problem …. please help?
so I have absolutely no clue what I'm supposed to be doing word problem …… – A long sheet of metal, 16 inches wide, both sides appeared to make a horizontal channel with vertical sides. How many inches should be increased on each side of the maximum load? please help …. details I do not want the answer only
what we are trying to do is maximize the cross-sectional area of a rectangle the size of the rectangle be x vertical, and 16 – 2x horizontal (as the metal is 16 inches wide, two pieces each 16 x vertical sheets – 2x for the area of the horizontal X = b * h = (16 – 2x) This is the feature you are trying to maximize ..|………. …..| ..|……….. X ..|……………| ..————- ….| …. 16 – 2x (16 – 2x) + x + x = 16 = Total area wide x (16 – 2x) = 16x – 2x ^ 2 The vertex is, maximum since this parabola opens downwards zeros at x = 0 and x = 8, the vertex is halfway between those at x = 4 = 4 vertical sides, horizontal bottom = 16-8 = 8 so that the maximum capacity is 4 * 8 = 32 square inches of verification section calculation: A = 16x – 2x ^ 2 A '= 16 – 4x A '= 0 at x = 4 A (4) = 64-32 = 32 A = -4, so this is a maximum
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