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A solid rectangular block has a square base of side x cm. The height of the block is h cm and the total surface area of the block is 96 cm². Given that x can vary, find the stationary value of the volume V, and determine whether this value is a maximum or a minimum. and at time t seconds is 0°C.

Respuesta :

Answer:

S = 2x² + 4xh = 96

x² + 2xh = 48

2xh = 48 - x²

h = 24/x - x/2

V(x) = x²h = x²(24/x - x/2)

= 24x - x³/2

V'(x) = 24 - 3x²/2 = 0

24 = 3x²/2

3x² = 48

x² = 16

x = 4

V(4) = 24(4) - 4³/2 = 96 - 32 = 64

V"(x) = -6x > 0 for all x > 0

So this is a maximum volume.

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