As I just have my test. I found this kind of problem :

Which one of these have a biggest value?

A. \(99^{100}\)

B. \(98^{101}\)

C. \(105^{97}\)

D. \(101^{98}\)

E. \(100^{99}\)

I will appreciate any feedbacks. Thanks.

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## Comments

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TopNewestHint:- Look at the function \( f(x) = x^{199 - x} \)

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so how can i use that function to find it ?

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\( f'(x) = x^{199 - x}(-\ln{x} + \frac{109 -x}{x}) \).

In [98,105], we have \( \ln{x} > 1 > \frac{109-x}{x} \). So \( f'(x) < 0 \), which means that \( f(x) \) decreasing in [98,105]. So the maximum value occurs at the smallest \( x \), i.e., 98^101.

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