Consider two functions of time (t), f(t) = 0.01\,t^2, g(t) = 4\,t where 0 0, g(t) > f(t). (ii) There exists a T, such that f(t) > g(t) for all t > T. Which one of the following options is TRUE?

neither (i) nor (ii) is correct

GATE CSE 2023 Q7: Comparing f(t) = 0.01t² and g(t) = 4t

Consider two functions of time ( $t$ ),

$f(t) = 0.01\,t^2, \qquad g(t) = 4\,t$

where $0 < t < \infty$ .

Now consider the following two statements:

(i) For some $t > 0$ , $g(t) > f(t)$ .

(ii) There exists a $T$ , such that $f(t) > g(t)$ for all $t > T$ .

Which one of the following options is TRUE?

Try it: multiple choice: exactly one correct option

Wrong answer costs 2/3 mark in GATE.

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Answer: C (official GATE 2023 final answer key)

Concept used: A quadratic eventually overtakes a linear function, but the linear one can be larger for small $t$ .

First step: Solve $0.01t^2 = 4t$ to find where the two curves cross ( $t = 400$ ).

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Source: official GATE 2023 CS question paper and final answer key, organised by IIT Kanpur. Question paper · Answer key