Exams › JEE Advanced › Maths

Which of the following represents the correct pairing?

1. Smoothly connected but not having a derivative
2. Smoothly connected and having a derivative
3. Having a derivative but not smoothly connected
4. Neither smoothly connected nor having a derivative

Correct answer: Smoothly connected but not having a derivative

Solution

A function may be continuous (smoothly connected) at a point without being differentiable there, for example at a cusp or corner. So the correct pairing is continuity without differentiability.

Related JEE Advanced Maths questions

• Let \(f:[-2a,2a]\to \mathbb{R}\) be an odd function. If the left-hand derivative at \(x=a\) is zero and \(f(x)=f(2a-x)\) for all \(x\in(a,2a)\), what is the value of the left-hand derivative at \(x=-a\)?
• If \(f\) is a differentiable function such that \([f(x)]^n=f(nx)\) for every real number \(x\), what is the value of \(\frac{f'(x)}{f(x^n)}\)?
• If \(f(x)=\begin{cases}(\sin^{-1}x)^2\cos(1/x), & x\ne 0\\0, & x=0\end{cases}\), then
• For $0<p\le 1$, analyze whether the function $f(x)=\begin{cases}x^p\sin(1/x), & x\ne 0\\0, & x=0\end{cases}$ is continuous and differentiable at $x=0$.
• For the function $f(x)$ defined on the interval $[-3,3]$ by $f(x)=\max\{\sqrt{9-x^2},\sqrt{1+x^2}\}$ for $-3\le x\le 0$, which of the following is true?
• If (f'(x)\le 0) for all (x) in the interval ([0,b]), and (f(c)=0), then (f(x)) intersects the x-axis only once at (x=c). What is true about the root at (x=c)?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →