As MarkFL pointed out, you can have f(0)= 16 or -3 but not both.thinkbot said:f(x) = {
{ 16 - x^2, if -4 <= x <= 0
{ 2x - 3, if 0 <= x <= 4
I did the first derivative test and got zero but i don't think that's right. Any help?
In order to identify a piecewise function in your data, you will first need to look for any discontinuities or changes in the function's behavior. These changes will typically occur at specific values of the independent variable, such as a sharp turn or a sudden increase/decrease. Once you have identified these changes, you can then determine the different segments of the piecewise function.
The best way to determine the local minima in a piecewise function is to graph the function and visually identify where it reaches its lowest points. You can also take the derivative of the function and set it equal to zero, then solve for the independent variable to find the x-values of the local minima. Alternatively, you can use a graphing calculator or software to help you find the local minima.
Yes, a piecewise function can have multiple local minima. This means that there can be multiple points in the function where the slope is equal to zero and the function reaches its lowest value. It is important to carefully examine the shape of the function and its different segments to identify all of the local minima.
Yes, there are a few techniques that can be helpful in finding the local minima in a piecewise function. These include using the first or second derivative tests, graphing the function, or using a calculator or software to find the local minima. It is important to use multiple methods to verify the accuracy of your results.
Yes, it is possible for a piecewise function to have no local minima. This would occur when the function is either constantly increasing or constantly decreasing, and does not have any points where the slope is equal to zero. In this case, there are no local minima in the function.