What number exceeds its square by the largest amount? [Hint:

villane0

villane0

Answered question

2021-11-16

What number exceeds its square by the largest amount? [Hint: Find the number x that maximizes f(x)=xx2.]

Answer & Explanation

Opeance1951

Opeance1951

Beginner2021-11-17Added 26 answers

Let the number is x, then
f(x)=xx2
The goal is to find the absolute maximum of this function.
Since f(x)=12x1
Then f(x)=0 for x=0.5 and
f(x)=2f(0.5)<0
Hence an absolute maximum point occurs for the given value of x and
f(0.5)=0.25

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