Electrical Circuit: Finding Max/Min Voltage in 5 min

AI Thread Summary
The voltage in the given electrical circuit is represented by the equation V = 12 - 9t + 2t^2. The maximum voltage of 17 V occurs at 5 minutes, while the minimum voltage is 1.875 V at 2.25 minutes. To find these values, one can analyze the parabolic graph of the equation or calculate the vertex by using the derivative. The discussion emphasizes the importance of understanding how to derive both maximum and minimum values in a quadratic function. This approach is essential for solving similar problems in electrical circuits.
Koyuki
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The problem is:
"In an electrical circuit, the voltage, V volts, as a function of time, t minutes, is given by V = 12 - 9t + 2t^2. Determine the greatest and least values of voltage during the first 5 min. When do these values occur?"

The answers given are exact.
Least: 1.875 V @ 2.25 min
Most: 17 V @ 5 min

Well I know how to get the max, but the min?

Thanks!
 
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Koyuki said:
...
Well I know how to get the max, but the min?
...
The graph is a parabola. You can find the vertex if you remember how, or you can find where the derivative is 0.
 
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