Questions: V=3 I^2+6 I-2 a）求这仝。（4個步语） d）最少电蓢時，电流工是多少？(dv/dI=0) e）最少电愿，V？（把d）的答亲，代入問题）

Transcript text: V=3 I^{2}+6 I-2 a）求这仝。（4個步语） d）最少电蓢時，电流工是多少？$\left(\frac{d v}{d I}=0\right)$ e）最少电愿，V？（把d）的答亲，代入問题）

Solution

Solution Steps

Step 1: Finding the Critical Point

To find the current $ I $ at which the voltage $ V $ is minimized, we first compute the derivative of $ V $ with respect to $ I $: \[ \frac{dV}{dI} = 6I + 6 \] Setting the derivative equal to zero to find the critical points: \[ 6I + 6 = 0 \implies I = -1 \]

Step 2: Calculating the Minimum Voltage

Next, we substitute the critical point $ I = -1 $ back into the original voltage equation: \[ V = 3(-1)^2 + 6(-1) - 2 = 3 - 6 - 2 = -5 \]