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The temperature of a city in summer is modeled by T(x) = 40 - 6*(x - 6)^2 where x is...

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lxsptter | Student, Undergraduate | Valedictorian

Posted May 24, 2013 at 2:49 AM via web

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The temperature of a city in summer is modeled by T(x) = 40 - 6*(x - 6)^2 where x is the number of hours after 6 AM. When is the temperature the highest.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 24, 2013 at 2:58 AM (Answer #1)

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The temperature measured during a day in summer can be modeled by the function T(x) = 40 - 6*(x - 6)^2 where x is the number of hours after 6 AM.

This can be represented as a graph of temperature versus time as follows:

The graph is a parabola with temperature rising, reaching a maximum and then dropping.

If the temperature is at the maximum t hours after 6 AM. T'(t) = 0 and T''(t) < 0.

As T(x) = 40 - 6*(x - 6)^2, T'(x) = -12*(x - 6) and T''(x) = -12.

T'(t) = 0

=> t = 6

And T''(6) is negative.

The temperature is at the maximum at 12 PM.

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