Express maximum as an equation

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SUMMARY

The maximum of two variables A and B can be expressed using the equation MAXIMUM(A, B). This can be represented as a piecewise function, which explicitly defines the maximum based on the values of A and B. When given a third variable C, where MAXIMUM(A, B) = C, it is impossible to uniquely solve for A if B is greater than A, as A can take any value less than C. The derived equation a*((a-b)/abs(a-b)+1)/2+b*((b-a)/abs(b-a)+1)/2 is valid when A and B are not equal.

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  • Understanding of piecewise functions
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  • Basic algebraic manipulation skills
  • Knowledge of maximum functions in mathematics
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  • Learn about absolute value properties and their implications in equations
  • Explore maximum and minimum functions in calculus
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Given variables A and B
How is the maximum of A and B expressed as an equation?
Another way of saying it is how do you express MAXIMUM(A,B) as an equation?

Given variables A,B,C
MAXIMUM(A,B)=C
How do you solve for A?
 
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Crusty said:
Given variables A and B
How is the maximum of A and B expressed as an equation?
Another way of saying it is how do you express MAXIMUM(A,B) as an equation?

Given variables A,B,C
MAXIMUM(A,B)=C
How do you solve for A?

For part 1, you can write a piecewise function but it is just typing out what maximum means.

For the second part, you can't necessarily recover A from C. Suppose that B>A. Then A could be any value less than C.
 
Last edited:
How do you write it piecewise again?

For writing as an equation, I came up with this but it only works when the numbers aren't equal
a*((a-b)/abs(a-b)+1)/2+b*((b-a)/abs(b-a)+1)/2
 

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