When do we have both minimum and maximum values?
So, if we have a continuous function on an interval [a,b] [ a, b] then we are guaranteed to have both an absolute maximum and an absolute minimum for the function somewhere in the interval. The theorem doesn’t tell us where they will occur or if they will occur more than once, but at least it tells us that they do exist somewhere.
Which is function does not have an absolute maximum?
So, the function does not have an absolute maximum. Note that it does have an absolute minimum however. In fact the absolute minimum occurs twice at both x =−1 x = − 1 and x =1 x = 1. the function would now have both absolute extrema.
How to find the maximum value in an array?
Given an array of integers which is initially increasing and then decreasing, find the maximum value in the array. Recommended: Please solve it on “ PRACTICE ” first, before moving on to the solution.
Can a graph have maximums but not minimums?
So, some graphs can have minimums but not maximums. Likewise, a graph could have maximums but not minimums. Here is the graph for this function. This function has an absolute maximum of eight at x = 2 x = 2 and an absolute minimum of negative eight at x = − 2 x = − 2.
Is there an absolute minimum or a local maxima?
We say has a local maximum at Similarly, the function does not have an absolute minimum, but it does have a local minimum at because is less than for near 1. Figure 3. This function has two local maxima and one local minimum.
Is it easy to see a local maximum or local minimum?
Given the graph of a function it is sometimes easy to see where a local maximum or local minimum occurs. However, it is not always easy to see, since the interesting features on the graph of a function may not be visible because they occur at a very small scale. Also, we may not have a graph of the function.
Is there an absolute maximum or a local minimum for F?
We say f has a local maximum at x = 0. Similarly, the function f does not have an absolute minimum, but it does have a local minimum at x = 1 because f(1) is less than f(x) for x near 1. Figure 4.1.3: This function f has two local maxima and one local minimum. The local maximum at x = 2 is also the absolute maximum.