- #1
Albert1
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find minimum value of $f$
given :
$(1)a,b,c,x,y\in R^+$
$(2)x+y=c$
$(3)f=\sqrt {a^2+x^2}+\sqrt {b^2+y^2}$
find :$min (f)$
given :
$(1)a,b,c,x,y\in R^+$
$(2)x+y=c$
$(3)f=\sqrt {a^2+x^2}+\sqrt {b^2+y^2}$
find :$min (f)$
using geometryAlbert said:find minimum value of $f$
given :
$(1)a,b,c,x,y\in R^+$
$(2)x+y=c$
$(3)f=\sqrt {a^2+x^2}+\sqrt {b^2+y^2}---(1)$
find :$min (f)$
The minimum value of a function, denoted as f(min), is the smallest possible output value of the function within a given domain.
To find the minimum value of a function, you can set its derivative equal to 0 and solve for the input variable, or use graphical methods such as a graphing calculator or software.
Finding the minimum value of a function is important because it helps identify the most optimal or efficient solution to a problem, and can provide insights into the behavior and relationships of variables in a system.
Yes, a function can have multiple minimum values if it has multiple local minima. In this case, each minimum value represents a different optimal solution.
A global minimum is the absolute lowest value of a function within its entire domain, while a local minimum is the lowest value within a specific interval. To determine if a minimum value is global or local, you can examine the behavior of the function and its derivative at different points.