# Thread: Need help in finding the maximum

1. ## Need help in finding the maximum

I need help in finding the maximum of this equation:
V(t)=2580+300cos(t*138.23007)

I found the derivative to be:
V'(t)=-41469.02100*sin(138.23007*t)

I just can't figure out how to find the maximum, please help. Thanks!

2. Originally Posted by Theressa
I need help in finding the maximum of this equation:
V(t)=2580+300cos(w*138.23007)

I found the derivative to be:
V'(t)=-41469.02100*sin(138.23007*t)

I just can't figure out how to find the maximum, please help. Thanks!

As you can see, in the definition of V(t) there is no t in the right hand, so its derivative would be zero!
I'm sure there's a typo somewhere but I can't say where.

Tonio

3. Originally Posted by tonio
As you can see, in the definition of V(t) there is no t in the right hand, so its derivative would be zero!
I'm sure there's a typo somewhere but I can't say where.

Tonio
Sorry about that, the w is supposed to be a t. My mistake.

4. Originally Posted by Theressa
I need help in finding the maximum of this equation:
V(t)=2580+300cos(t*138.23007)

I found the derivative to be:
V'(t)=-41469.02100*sin(138.23007*t)

I just can't figure out how to find the maximum, please help. Thanks!

Well, this is ugly, but you have to equal the derivative to zero and find out when that happens:

$V'(t)=-41,469.021*\sin (138.23007t)=0 \Longrightarrow138.23007t=n\pi$, for some integer multiple of $\pi$ , so $t=\frac{n\pi}{138.23007}$

The value for n you'll get from, perhaps, other conditions on the problem.

Tonio