Consider the functions I. e^-x II. x^2 - x III. x^3 + 1 Which of the above functions is/are increasing everywhere in [0,1]?

GATE CSE 2020 Q11: Which functions are increasing everywhere in [0, 1]

Consider the functions

I. $e^{-x}$

II. $x^2 - \sin x$

III. $\sqrt{x^3 + 1}$

Which of the above functions is/are increasing everywhere in $[0,1]$ ?

Try it: multiple choice: exactly one correct option

Wrong answer costs 1/3 mark in GATE.

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Answer: A (official GATE 2020 final answer key)

Concept used: A function is increasing on an interval where its derivative is non-negative throughout.

First step: Differentiate each: $-e^{-x}$ , $2x - \cos x$ (check its sign at $x = 0$ ), and $\frac{3x^2}{2\sqrt{x^3+1}}$ .

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Source: official GATE 2020 CS question paper and final answer key, organised by IIT Delhi. Question paper · Answer key