You may know Differential calculus, but Don't lie completely on it!

Calculus Level 2

f ( x ) = x x 2 + 1 f(x) = \frac{x}{x^{2} + 1}

x is a positive real number

what is its maximum value?

maximum value is of the form a b \frac{a}{b}

find the value of a + b


The answer is 3.

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U Z by U Z , 24, Guyana

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2 solutions

U Z
Oct 22, 2014

f ( x ) = 1 x + 1 x f(x) = \frac{1}{ x + \frac{1}{x}}

For f ( x ) f(x) to be maximum denominator should be minimum

thus m i n ( x + 1 x ) = 2 min( x + \frac{1}{x}) = 2

thus m a x ( f ( x ) ) = 1 2 max(f(x)) = \frac{1}{2}

16 Helpful 0 Interesting 0 Brilliant 0 Confused

2x/(x^2+1)=sin t

so, expression becomes ( sin t )/2

max value is 1/2

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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