Example Application
Consider the function
for all positive real numbers x, y and z. Suppose we wish to find the minimal value of this function. First we rewrite it a bit:
with
Applying the AM–GM inequality for n = 6, we get
Further, we know that the two sides are equal exactly when all the terms of the mean are equal:
All the points (x,y,z) satisfying these conditions lie on a half-line starting at the origin and are given by
Read more about this topic: Inequality Of Arithmetic And Geometric Means
Famous quotes containing the word application:
“The human mind is capable of excitement without the application of gross and violent stimulants; and he must have a very faint perception of its beauty and dignity who does not know this.”
—William Wordsworth (17701850)
“If you would be a favourite of your king, address yourself to his weaknesses. An application to his reason will seldom prove very successful.”
—Philip Dormer Stanhope, 4th Earl Chesterfield (16941773)