JEE Main 2014 · 19 Apr · Shift 1 · Mathematics Q71

← JEE Main 2014 · 19 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 71 of 90

Let $f:\mathbb R\to\mathbb R$ be a function such that $|f(x)|\le x^2$ , for all $x\in\mathbb R$ . Then, at $x=0$ , $f$ is :

continuous but not differentiable

continuous as well as differentiable

neither continuous nor differentiable

differentiable but not continuous.

Answer and worked solution

Official answer: B

$|f(0)|\le0$ gives $f(0)=0$ , and $|f(x)|\le x^2\to0$ , so $f$ is continuous. Also $\left|\dfrac{f(h)-f(0)}h\right|\le|h|\to0$ , so $f'(0)=0$ : continuous and differentiable.

Topics:Differentiability Continuity

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JEE Main 2014 · 19 Apr · Shift 1, Mathematics question 71