Some textbooks distinguish between maximum and maximum value, and similarly for minimum and minimum value. Here maximum or minimum refer to the x-value, while maximum value or minimum value refer to the function value.zeion said:Homework Statement
Name two different functions that share a maximum and minimum at -4.
Homework Equations
The Attempt at a Solution
This is a vague question. I guess horizontal lines would be one. I can't think of another.
A function that is always a point?
I believe that was what zeion said in his original post. The problem is to find another function that has the same number as maximum and minimum.zgozvrm said:How about f(x) = -4 ?
int(x) has jump discontinuities at each x ε Z, and yet, at every "step" (look at the graph) every point is considered to be both a local minimum and a local maximum.AGNuke said:No local Min or Max for discontinuous functions as I believe. Main is whether the min/max value or minima and maxima (which corresponds to x)
(The book also has a similar definition for a local minimum)A local maximum of a function f is a value f(c) that is greater than or equal to all range values of f on some open intervale containing c. If f(c) is greater than or equal to all range values in f, then f(c) is the maximum (or absolute maximum) of f.
Finding a function with the same maximum and minimum means that the function has the same highest and lowest values. In other words, the maximum and minimum values occur at the same input or x-value.
Finding a function with the same maximum and minimum can be important in various applications, such as optimization problems in mathematics and engineering. It can also provide insight into the behavior of a function and its critical points.
No, not all functions can have the same maximum and minimum. For example, a linear function with a positive slope will have a different maximum and minimum, whereas a constant function will have the same maximum and minimum.
There are various methods to find a function with the same maximum and minimum. One approach is to use calculus and find the critical points of the function. Another method is to graph the function and observe where the maximum and minimum occur.
Yes, there are real-life examples of functions with the same maximum and minimum. One example is a Ferris wheel, where the maximum and minimum heights occur at the same point. Another example is a bouncing ball, where the maximum and minimum heights are the same if the ball bounces vertically.