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GATE 2020 CS – Question 11

Engineering Mathematics · Calculus · 1 mark · Multiple choice

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 $[0,1]$?

  1. III only
  2. II only
  3. II and III only
  4. I and III only

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Correct answer: (A) III only

Explanation

$e^{-x}$ is decreasing. For $x^2-\sin x$ the derivative $2x-\cos x$ is $-1$ at $x=0$, so it decreases near 0. $\sqrt{x^3+1}$ has derivative $\frac{3x^2}{2\sqrt{x^3+1}}\ge 0$, so it is increasing. Answer: III only.