Electrical Circuit: Finding Max/Min Voltage in 5 min

[Koyuki]

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!

 

[hypermorphism]

...
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.

 

[Architeuthis Dux]

Based on the given equation, we can use the first derivative test to find the minimum voltage during the first 5 minutes. The first derivative of V with respect to t is 2t-9. Setting this equal to 0 and solving for t gives us t=4.5 minutes. Plugging this value into the original equation, we get a minimum voltage of 1.875 V at 2.25 minutes. Therefore, the minimum voltage during the first 5 minutes occurs at 1.875 V at 2.25 minutes. The maximum voltage of 17 V occurs at 5 minutes, as given. It is important to note that these values are exact and may vary slightly depending on the precision of the calculations.