Question

The function f (x) = x², for all real x, is ____________.

Options

• Decreasing

• Neither decreasing nor increasing

• Increasing

• None of these

Answer 1

The function f (x) = x², for all real x, is Neither decreasing nor increasing.

Explanation:

f(x) = x²

⇒ f'(x) = 2x for all x in R.

Since f‘ (x) = 2x > 0 for x > 0, and f‘ (x) = 2x < 0 for x < 0, therefore on R, f is neither increasing nor decreasing. Infact, f is strict increasing on `[ 0,infty)  "and strict decreasing on" (-infty,0]`.