Why e maximizes the product

This is an optimization proof of my claim that e is the best number to add up to make a positive number ( greater than e) if the maximum product is required.

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p² - p +1 = n³
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p² - p +1 = n³

Find C if f(f(x)) has 3 distinct real roots
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Find C if f(f(x)) has 3 distinct real roots

What Lies *Between* a Function and Its Derivative?
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What Lies *Between* a Function and Its Derivative?

Compute the largest number
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Compute the largest number

Mysterious Kaprekar's Constant: Glitch or Pattern?
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Mysterious Kaprekar's Constant: Glitch or Pattern?

We're 99.9% sure this pattern is true, but no one can prove it
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We're 99.9% sure this pattern is true, but no one can prove it

Find all real x
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Find all real x

a * b = ab + a + b
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a * b = ab + a + b

Square root of imaginary number.
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Square root of imaginary number.

Find all positive integer n
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Find all positive integer n

Why Does Time Stop at the SPEED OF LIGHT? Feynman's Mind-Blowing Truth
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Why Does Time Stop at the SPEED OF LIGHT? Feynman's Mind-Blowing Truth

Greatest Chess Engine Match Ever Played
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Greatest Chess Engine Match Ever Played

Is this limit actually solvable? Tricky calculus 1 limit. Reddit r/askmath
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Is this limit actually solvable? Tricky calculus 1 limit. Reddit r/askmath

But what is a Laplace Transform?
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But what is a Laplace Transform?

a+b+c+d+e = abcde
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a+b+c+d+e = abcde

if x+y=8, find the max of x^y (Lambert W function)
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if x+y=8, find the max of x^y (Lambert W function)

When Math Isn’t Based in Reality
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When Math Isn’t Based in Reality

Is It Really Impossible To Pull Apart Two Interleaved Phone Books? | MythBusters
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Is It Really Impossible To Pull Apart Two Interleaved Phone Books? | MythBusters

Prove that (1/x + 1/y + 1/z) is greater than 3
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Prove that (1/x + 1/y + 1/z) is greater than 3

Find all natural numbers for which n^10 + n^5 +1 is prime
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Find all natural numbers for which n^10 + n^5 +1 is prime