Question

x^5x has a stationary point at ______.

Options

• x = e

• x = `1/"e"`

• x = 1

• x = `sqrt("e")`

Answer 1

x^5x has a stationary point at x = `1/"e"`.

Explanation:

Let y = x^5x 

⇒ `log y = 5x . log x, (x > 0)`

Differentiating, `("d"y)/("d"x) = 5x^(5x)(1 + log x);`

∴ `("d"y)/("d"x)` = 0

⇒ `log x = -1`

⇒ x = `"e"^-1 = 1/"e"`

∴ Stationary point is x = `1/"e"`