What is bigger: 3^π or π³?

Let's explore why 3^π is greater than π³ and discover the global maximum at Euler's number.

Comparing the Values

First, let's calculate both values and see which one is larger.

The General Pattern: x^π vs π^x

Let's visualize the function f(x) = x^π - π^x to understand when x^π is greater than π^x.

Finding the Maximum: Euler's Number

The global maximum of x^(1/x) occurs at Euler's number e ≈ 2.718.

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