Exponential Function Question (1 Viewer)

RivalryofTroll · Nov 4, 2012

f(x) = (log(e)x)/x

Use the fact that the maximum value of f(x) occurs at x = e, deduce that:

e^x >= x^e for all x>0

RealiseNothing · Nov 4, 2012

The maximum value of f(x) is 1/e, so we can say that:

$f(x) \leq \frac{1}{e}$

$\frac{ln(x)}{x} \leq \frac{1}{e}$

$e.ln{(x)} \leq x$

$ln{(x^e)} \leq x$

$x^e \leq e^x$

$e^x \geq x^e$

Exponential Function Question (1 Viewer)

RivalryofTroll

Sleep Deprived Entity

RealiseNothing

what is that?It is Cowpea

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