# Find local maximum value

1. Sep 3, 2015

### cloveryeah

1. The problem statement, all variables and given/known data
y=(8/5)sint + (4/5) cost - (9/5)e^(-t/2)

find its local max
2. Relevant equations

3. The attempt at a solution
i have differentiated it and found out dy/dx,
in order to find the local max, i have to find out the value t when dy/dx=0
but i cant solve this equation

2. Sep 3, 2015

### RUber

Local in what neighborhood? I don't see any x in the problem you posted, what is dy/dx?
Note that as t gets large, you can neglect the exponential term. Then you can easily solve the trigonometric equation.

3. Sep 3, 2015

### Ray Vickson

Of course, dy/dx = 0 because your y does not contain any x variable. However, if you mean dy/dt then I agree, you have an "unsolvable" problem, in the sense that there will be no nice closed-from solution. However, you can use numerical methods.

In such cases, always start by plotting a graph of your function, to get a feel for what is happening. Plotting the derivative can be helpful, too.

BTW: your post is mis-named. You do not have a differential equation, you just have a given function that you want to differentiate.

4. Sep 3, 2015