Question:
The maximum value of $\frac{log_ex}{x}$, if x > 0 is
The maximum value of $\frac{log_ex}{x}$, if x > 0 is
Updated On: May 19, 2024
- $e$
- $1$
- $\frac{1}{e}$
- $- \frac{1}{e}$
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The Correct Option is C
Solution and Explanation
$(y = \frac{log_e \ x}{x})$
$? \left(\frac{dy}{dx}=\frac{1 - log_e x}{x^2}\right)$
For maxima, $dy/dx = 0$
$? 1 - log_e x = 0$
$? x = e$
$dy/dx$ changes sign from positive to negative at $x = e$
$? y_{\text{max}} = 1/e$
$? \left(\frac{dy}{dx}=\frac{1 - log_e x}{x^2}\right)$
For maxima, $dy/dx = 0$
$? 1 - log_e x = 0$
$? x = e$
$dy/dx$ changes sign from positive to negative at $x = e$
$? y_{\text{max}} = 1/e$
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Concepts Used:
Maxima and Minima
What are Maxima and Minima of a Function?
The extrema of a function are very well known as Maxima and minima. Maxima is the maximum and minima is the minimum value of a function within the given set of ranges.
There are two types of maxima and minima that exist in a function, such as:
- Local Maxima and Minima
- Absolute or Global Maxima and Minima