Find the maximum of Planck's radiation function

Example 2 steps, run in order in one session. Every step was executed against the engine and the output below is what it produced.

Step 1

P = (15/π^4 (x^5 (Exp[(1/x)] - 1)));
{max, val} = Maximize[{P, x ≥ 0}, x]

Output

{Infinity, {x -> Infinity}}

Step 2

Plot[P, {x, 0, 1}, Epilog -> {Red, PointSize[0.025], Point[{x /. val, max}]}]

Output

-Graphics-

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Functions used

Exp Maximize Plot Point PointSize

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