Question

The function f(x) = x² – 2x is increasing in the interval ____________.

Options

• `"x" ge 1`

• `"x" ge -1`

• `"x" ne 1`

• `"x" ne -1`

Answer 1

The function f(x) = x² – 2x is increasing in the interval `underline("x" ge 1)`.

Explanation:

`"f"("x") = "x"^2 - 2"x"`

`=> "f'"("x") = 2"x" - 2 = 2("x" - 1)`

So , f(x) is increasing if `2("x" - 1) ge 0`, i.e. if `"x" ge 1`