JEE Mains · Maths · STD 12 - 5. continuity and differentiation
The number of points, at which the function \(f ( x )\) \(=|2 x+1|-3|x+2|+\left|x^{2}+x-2\right|, x \in R\) is not differentiable, is ............
- A \(6\)
- B \(8\)
- C \(2\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(f(x)=|2 x+1|-3|x+2|+\left|x^{2}+x-2\right|\) \(=|2 x+1|-3|x+2|+|x+2||x-1|\) \(=|2 x+1|+|x+2|(|x-1|-3)\) Critical points are \(x=\frac{-1}{2},-2,-1\) but \(x=-2\) is making a zero. twice in product so, points of non differentability are \(x =\frac{-1}{2}\) and \(x =-1\)…
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
- The following system of linear equations \(7 x+6 y-2 z=0\) ; \(3 x+4 y+2 z=0\) ; \({x}-2{y}-6{z}=0,\) hasJEE Mains 2020 Hard
- If \({\cos ^{ - 1}}\left( {\frac{2}{{3x}}} \right) + {\cos ^{ - 1}}\,\left( {\frac{3}{{4x}}} \right) = \frac{\pi }{2},\,x > \frac{3}{4}\) then \(x\) is equal toJEE Mains 2019 Hard
- Let \(\vec{b}=\hat{i}+\hat{j}+\lambda \hat{k}, \lambda \in R\). If \(\vec{a}\) is a vector such that \(\overrightarrow{ a } \times \overrightarrow{ b }=13 \hat{ i }-\hat{ j }-4 \hat{ k } \quad\) and \(\quad \overrightarrow{ a } \cdot \overrightarrow{ b }+21=0\), then \((\vec{b}-\vec{a}) \cdot(\hat{k}-\hat{j})+(\vec{b}+\vec{a}) \cdot(\hat{i}-\hat{k})\) is equal toJEE Mains 2022 Medium
- The value of \(\int\limits_0^{\pi /2} {\frac{{{{\sin }^3}\,x}}{{\sin \,x\, + \,\cos \,x}}} \,dx\) isJEE Mains 2019 Hard
- Let \(\alpha, \beta \in \mathbb{R}\) be such that the system of linear equations
\(x + 2y + z = 5\)
\(2x + y + \alpha z = 5\)
\(8x + 4y + \beta z = 18\)
has no solution. Then \(\dfrac{\beta}{\alpha}\) is equal to :JEE Mains 2026 Medium - Let \(f\) be a twice differentiable function on \((1,6) .\) If \(f (2)=8, f ^{\prime}(2)=5, f ^{\prime}( x ) \geq 1\) and \(f ^{\prime \prime}( x ) \geq 4,\) for all \(x \in(1,6),\) thenJEE Mains 2020 Medium
More PYQs from JEE Mains
- Let \(y=y(x)\) be the solution of the differential equation \(x\frac{dy}{dx}-y=x^{2}\cot x, x\in(0,\pi)\). If \(y(\frac{\pi}{2})=\frac{\pi}{2}\), then \(6y(\frac{\pi}{6})-8y(\frac{\pi}{4})\) is equal to :JEE Mains 2026 Easy
- The area of the region enclosed by the curve \(y=x^3\) and its tangent at the point \((-1,-1)\) isJEE Mains 2023 Medium
- The point represented by \(2 + i\) in the Argand plane moves \(1\,unit\) eastwards, then \(2\,units\) northwards and finally from there \(2\sqrt 2\,units\) in the south-westwards direction. Then its new position in the Argand plane is at the point represented byJEE Mains 2016 Hard
- Let \(\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1\) and \(\vec{a} \times \vec{b}=\hat{i}-\hat{j}\). Then \(\vec{a}-6 \vec{b}\) is equal toJEE Mains 2023 Medium
- The number of points where the function \(f(x)=\left\{\begin{array}{clr}\left|2 x^{2}-3 x-7\right| \, \text { if } x \leq-1 \\ {\left[4 x^{2}-1\right]} \text { if } -1 < x < 1 \\ |x+1|+|x-2| \text { if } x \geq 1\end{array}\right.\) \([t]\) denotes the greatest integer \(\leq t\), is discontinuous isJEE Mains 2022 Hard
- Let \(A = \left( {\begin{array}{*{20}{c}}
{\cos \,\alpha }&{ - \sin \,\alpha }\\
{\sin \,\alpha }&{\cos \,\alpha }
\end{array}} \right)\), \(\left( {\alpha \in R} \right)\) such that \({A^{32}} = \left( {\begin{array}{*{20}{c}}
0&{ - 1}\\
1&0
\end{array}} \right)\). Then a value of \(\alpha \) isJEE Mains 2019 Hard