# How do I find the upper bound of a function?

##### 1 Answer

Best way is to find it from the graph of the function.

#### Explanation:

The range of a function can be found in many ways , best way and a concrete way is by plotting its graph and determining.

How you draw the graph depends on you, a generic way is by differentiating the function to get the critical points or the points of maxima or minima . Then you double differentiate the function to see if the critical point is a maxima or minima by putting the critical point in the double differentiated function. If the output is positive then is a minima , if its negative then its a maxima and if its zero then the test fails,we have to go for high derivative tests. **The global maxima points give you the upper bound.**

Also we can determine the point of inflection for the given curve to determine the convexity or concavity changes of the given function to make the graph more precise .

Thus, having plotted the graph we can tell the upper bound of the function by merely looking at the maximum value of y for all values of x.

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