Home
Class 12
MATHS
The maximum value of (logx)/x is ...

The maximum value of `(logx)/x` is (a) `1` (b) `2/e` (c) `e` (d) `1/e`

A

`((1)/(e))`

B

`(2)/(e)`

C

`e`

D

1

Text Solution

AI Generated Solution

To find the maximum value of the function \( f(x) = \frac{\log x}{x} \), we will follow these steps: ### Step 1: Differentiate the function We start by differentiating \( f(x) \): \[ f'(x) = \frac{d}{dx} \left( \frac{\log x}{x} \right) \] Using the quotient rule, where \( u = \log x \) and \( v = x \): ...
Promotional Banner

Similar Questions

Explore conceptually related problems

The minimum value of x(log)_(e)x is equal to e (b) 1/e(c)-1/e (d) 2e( e )e

If f(x)= e^(coscos^-1x^2+tancot^-1 x^2), then minimum value of f(x) is (A) e (B) e^2 (C) e^(2/3 (D) none of these

The maximum value of x^((1)/(z)),x>0 is (a) e^((1)/(e))(b)((1)/(e))^(e)(c)1(d) none of these

The minimum value of (x)/((log)_(e)x) is e(b)1/e(c)1(d) none of these

Show that the maximum value of ((1)/(x))^(x) is e^(1/e)

If y=e^( sinx ) the value of (dy)/(dx) at x=(pi)/(2) is , (a) 1 , (b) e , (c) 0 ,(d) not defined .

a, b, c, d and e are integers .If a, b, c, d and e are geometric progression and lcm(m, n) is the least common multiple of m and n, then the maximum value of (1)/(1cm (a,b)) + (1)/(1cm (b,c)) + (1)/(1cm(c,d)) + (1)/(1cm (d,e)) is

Show that the maximum value of ((1)/(x))^(x) is e^((1)/(e))

The value of lim_(xrarr0) (logx-1)/(x-e) , is

The minimum value of e^((2x^(2)-2x+1)sin^(2)x) is e(b)(1)/(e)(c)1(d)0