Question

The minimum value of the function f(x) = xlogx is ______.

Options

• `-1/e`

• – e

• `1/e`

• e

Answer 1

The minimum value of the function f(x) = xlogx is `underlinebb(-1/e)`.

Explanation:

f(x) = x log x 

∴ f'(x) = 1 + log x

For minimum value

f'(x) = 0 `\implies` 1 + log x = 0

`\implies` log x = – 1

`\implies` x = `1/e`

min value = `f(1/e) = 1/e.log(1/e)`

= `1/e(log1 - loge)`

= `1/e(0 - 1)`

= `-1/e`