Simple 5

Calculus Level 4

f ( x ) = 10 1 x / 2 x ! \large f(x) = \dfrac{101^{x/2}}{x!}

Find the value of x x such that f ( x ) f(x) is maximized.


The answer is 10.

Yash Dev Lamba by Yash Dev Lamba , 23, India

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1 solution

Amar Mavi
Jan 31, 2016

Let F[x]/F[x+1] = (x+1)/(101^{1/2}) so we find that for x = \sqrt{101} -1, F[x] = F[x+1] and x> \sqrt{101} -1 F[x] > F[x+1] so for x = Ceiling[ \sqrt{101} -1] F[x] can be maximized

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