JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The number of points, where the function \(f: R \rightarrow R , f ( x )=| x -1| \cos | x -2| \sin | x -1|+\) \((x-3)\left|x^{2}-5 x+4\right|\), is NOT differentiable, is.
- A \(1\)
- B \(2\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(f(x)=|x-1| \cos |x-2| \sin |x-1|+(x-3) \mid x^{2}-5 x +4 \mid\) \(=|x-1| \cos |x-2| \sin |x-1|+(x-3)|x-1||x-4|\) \(=|x-1|[\cos |x-2| \sin |x-1|+(x-3)|x-4|]\) Non differentiable at \(x =1\) and \(x =4\).
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let A be a \(3\times3\) matrix such that \(A+A^{T}=O\). If \(A\begin{bmatrix}1\\ -1\\ 0\end{bmatrix}=\begin{bmatrix}3\\ 3\\ 2\end{bmatrix}\), \(A^{2}\begin{bmatrix}1\\ -1\\ 0\end{bmatrix}=\begin{bmatrix}-3\\ 19\\ -24\end{bmatrix}\) and \(\det(adj(2adj(A+I)))\) = \((2)^\alpha \cdot(3)^\beta \cdot(11)^\gamma\), then \(\alpha+\beta+\gamma\) is equal to ___ .JEE Mains 2026 Medium
- Let \(N\) be the sum of the numbers appeared when two fair dice are rolled and let the probability that \(N -2, \sqrt{3 N }, N +2\) are in geometric progression be \(\frac{ k }{48}\). Then the value of \(k\) isJEE Mains 2023 Hard
- Let \(\mathrm{a}_{\mathrm{n}}\) be the \(\mathrm{n}^{\text {th }}\) term of an A. P.
If \(S_n=a_1+a_2+a_3+\ldots+a_n=700, a_6=7\) and \(S_7=7\), then \(\mathrm{a}_{\mathrm{n}}\) is equal to :JEE Mains 2025 Medium - Let the foot of the perpendicular from the point \((1,2,4)\) on the line \(\frac{x+2}{4}=\frac{y-1}{2}=\frac{z+1}{3}\) be \(P.\) Then the distance of \(P\) from the plane \(3 x+4 y+12 z+23=0\)JEE Mains 2022 Medium
- For \(\mathrm{a}, \mathrm{b}>0\), let \(f(x)=\left\{\begin{array}{l}\frac{\tan ((a+1) x)+b \tan x}{x}, x<0 \\ \frac{\sqrt{a x+b^2 x^2}-\sqrt{a x}}{b \sqrt{a} x \sqrt{x}}, x>0\end{array}\right.\) be a continous function at \(x=0\). Then \(\frac{b}{a}\) is equal toJEE Mains 2024 Hard
- If the mirror image of the point \((1,3,5)\) with respect to the plane \(4 x -5 y +2 z =8\) is \((\alpha, \beta, \gamma)\) then \(5(\alpha+\beta+\gamma)\) equals ...... ..JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let \(P (a, b )\) be a point on the parabola \(y ^{2}=8 x\) such that the tangent at \(P\) passes through the centre of the circle \(x ^{2}+ y ^{2}-10 x -14 y +65=0\). Let \(A\) be the product of all possible values of \(a\) and \(B\) be the product of all possible values of \(b\). Then the value of \(A + B\) is equal to.JEE Mains 2022 Hard
- \(\operatorname{cosec} 18^{\circ}\) is a root of the equation :JEE Mains 2021 Hard
- The number of critical points of the function \(f(x)=(x-2)^{2 / 3}(2 x+1)\) is :JEE Mains 2024 Hard
- Let \( a_{1}=1 \) and for \( n\ge1 \), \( a_{n+1}\)
= \(\frac{1}{2}a_{n}+\frac{n^{2}-2n-1}{n^{2}(n+1)^{2}} \). Then \( |\sum_{n=1}^{\infty}(a_{n}-\frac{2}{n^{2}})| \) is equal to ........... .JEE Mains 2026 Easy - Let \(E\) and \(F\) be two independent events. The probability that both \(E\) and \(F\) happen is \(\frac{1}{12}\) and the probability that neither \(E\) nor \(F\) happens is \(\frac{1}{2}\) , then a value of \(\frac{{P(E)}}{{P\left( F \right)}}\) isJEE Mains 2017 Hard
- If \(\log _e \mathrm{a}, \log _e \mathrm{~b}, \log _e \mathrm{c}\) are in an \(A.P.\) and \(\log _e \mathrm{a}-\) \(\log _e 2 b, \log _e 2 b-\log _e 3 c, \log _e 3 c-\log _e a\) are also in an \(A.P,\) then \(a: b: c\) is equal toJEE Mains 2024 Hard