Show that the function f(x) = x2 is(a) strictly increasing on [0, ∞

1.	Show that the function f(x) = x2 is(a) strictly increasing on [0, ∞[(b) strictly decreasing on ]- ∞, 0[(c) neither strictly increasing nor strictly decreasing on R
Answer» (a) It is given that f(x) = x² By differentiating w.r.t x f’(x) = 2x > 0 for x ∈ (0, ∞) Here f’(x) > 0 which means 2x > 0 So we get x > 0 (b) We know that If f’(x) < 0 we get x < 0 (c) It is given that f(x) = x² is strictly increasing on [0, ∞[ and strictly decreasing on ]- ∞, 0[ So it is neither strictly increasing nor strictly decreasing on the whole real line.

Show that the function f(x) = x2 is(a) strictly increasing on [0, ∞[(b) strictly decreasing on ]- ∞, 0[(c) neither strictly increasing nor strictly decreasing on R

Answer»

(a) It is given that f(x) = x²

By differentiating w.r.t x

f’(x) = 2x > 0 for x ∈ (0, ∞)

Here f’(x) > 0 which means 2x > 0

So we get x > 0

(b) We know that

If f’(x) < 0 we get x < 0

(c) It is given that f(x) = x² is strictly increasing on [0, ∞[ and strictly decreasing on ]- ∞, 0[

So it is neither strictly increasing nor strictly decreasing on the whole real line.