# Maximum charge differential equation

1. Dec 10, 2011

### greg997

Hi, I am having a small problem with this equation

Charge Q=t^3+5t^2+10t+130

What is the maxiumum charge?
If I differentiate with repect to time, at t=6, for example then I have value of current flowing at that time.
What is the maximum charge then? I dont understand the question. Do I need to differentaite it again? Thanks

2. Dec 10, 2011

### grzz

At maximum Q, dQ/dt = 0.

But, so long as there is no mistake in the equation given, there is no value of t for which dQ/dt = 0.

3. Dec 10, 2011

### greg997

The equation has some value changed by me, but if dQ/dt=0 then the current is 0. Is that right?. About the equation, if I differentiate Q, then I can have two roots t. If I substitute them in the Q equation I have two real, different values. Is that right? Do I choose the higher value obtained?

4. Dec 10, 2011

### HallsofIvy

Staff Emeritus
A quadratic equation can have 2, 1, or no real roots. Read what grzz said again. Are there limits on the values of t?

5. Dec 10, 2011

### greg997

No, there are no limits.I know that quadratic equation can have 2,1, or no ral roots. But in this case it has two different real ones.

6. Dec 10, 2011

### Staff: Mentor

Each term on the right hand side increases with time, and these are all summed. So Q continuously increases with time. It will reach a maximum only at the end of time.
I think it's worth taking another look at the question. Something might be amiss.

7. Dec 10, 2011

### SammyS

Staff Emeritus
It asks for maximum charge, so just differentiate once. Yes, it so happens that when dQ/dt = 0 , in addition to having maximum (or minimum) charge, the current is also zero, because current = dQ/dt .