Gate2020 cs Q14
Which of the above functions is/are increasing everywhere in [0,1]?
- Option : D
- Explanation : (i) e–x is decreasing
(ii) f(x) = x2 – sinx
f′ (x) = 2x – cos x
Now check f′ (x) at [0, 1]
f′ (0) = –1
f′ (1) = 2 – cos 1 = 1.4596
∴ f(x) is not increasing everywhere
f′(x) ≥ 0 for all x.
∴ f(x) is an increasing function.
