cloveryeah said:Homework Statement
y=(8/5)sint + (4/5) cost - (9/5)e^(-t/2)
find its local max
Homework Equations
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 can't solve this equation
I changed the thread title...Ray Vickson said:BTW: your post is mis-named. You do not have a differential equation, you just have a given function that you want to differentiate.
A local maximum value is a point on a graph or function where the value is higher than all surrounding points, but not necessarily the highest value on the entire graph. It is also known as a peak or crest.
To find the local maximum value of a function, you can use the first or second derivative test. The first derivative test involves finding the critical points of the function and then checking the sign of the derivative at those points. If the derivative changes from positive to negative, then the point is a local maximum. The second derivative test involves finding the critical points and then evaluating the second derivative at those points. If the second derivative is negative, then the point is a local maximum.
A local maximum is a point on a graph or function where the value is higher than all surrounding points, but not necessarily the highest value on the entire graph. A global maximum, on the other hand, is the highest value on the entire graph or function. In other words, a global maximum is also a local maximum, but a local maximum is not always a global maximum.
Yes, a function can have more than one local maximum value. This occurs when the function has multiple peaks or crests. The number of local maximum values a function has is equal to the number of peaks or crests on the graph.
Finding the local maximum value is important because it allows us to identify the highest points on a graph or function. This can be useful in various real-world applications, such as determining the maximum profit in a business or the maximum temperature in a certain area. Additionally, understanding the behavior of a function at its local maximum values can provide insights into the overall behavior of the function.