Finding Differentiability using Differentiation
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Limits, Continuity and Differentiability

80241 Let \(f(x)=15-|x-10| ; x \in R\). Then, the set of all values of \(x\), at which the function, \(g(x)=\) \(\mathbf{f}(\mathbf{f}(\mathbf{x}))\) is not differentiable, is

1 \(\{5,10,15,20\}\)
2 \(\{5,10,15\}\)
3 \(\{10\}\)
4 \(\{10,15\}\)
JEE Main-2019-09.4.2019
Limits, Continuity and Differentiability

80242 If \(f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; |x| \geq 1 \\ a x^{2}+b ;|x|\lt 1\end{array}\right.\) is differentiable at every point of the domain, then the values of a and \(b\) are respectively

1 \(\frac{1}{2}, \frac{1}{2}\)
2 \(\frac{1}{2},-\frac{3}{2}\)
3 \(\frac{5}{2},-\frac{3}{2}\)
4 \(-\frac{1}{2}, \frac{3}{2}\)
JEE Main-2021-18.03.2021
Limits, Continuity and Differentiability

80243 The function that is not differentiable at \(x=1\) is

1 \(f_{1}(\mathrm{x})=|\mathrm{x}|,-\infty\lt \mathrm{x}\lt \infty\)
2 \(f_{2}(\mathrm{x})=\left\{\begin{array}{cc}1+\sin (\mathrm{x}-1), -\infty\lt \mathrm{x} \leq 1 \\ \mathrm{x}, \mathrm{x} \geq 1\end{array}\right.\)
3 \(f_{3}(x)=\left(\begin{array}{c}x^{2}+7 x-7,-\infty\lt x \leq 1 \\ \frac{3 x-1}{2}, x \geq 1\end{array}\right.\)
4 \(f_{4}(\mathrm{x})=\left\{\begin{array}{c}|\mathrm{x}-1|+|\mathrm{x}-2|,-\infty\lt \mathrm{x} \leq 1 \\ 1+\mathrm{x}-\mathrm{x}^{3}, \mathrm{x} \geq 1\end{array}\right.\)
TS EAMCET-2018-07.05.2018
Limits, Continuity and Differentiability

80244 The function \(f(x)=\left|x^{2}-2 x-3\right| \cdot e^{\left|9 x^{2}-12 x+4\right|}\) is not differentiable at exactly

1 four points
2 three points
3 two points
4 one point
JEE Main-2021-31.08.2021
Limits, Continuity and Differentiability

80245 \(f: R \rightarrow R\) is a function such that
\(|\mathbf{f}(\mathbf{x})-\mathbf{f}(\mathbf{y})| \leq \frac{\mathbf{1}}{\mathbf{2}}|\mathbf{x}-\mathbf{y}| \forall \mathbf{x}, \mathbf{y} \in \mathbf{R}\) and \(\mathbf{f}^{\prime}(\mathbf{x}) \geq \frac{1}{2}\) \(\forall \mathbf{x} \in \mathbf{R}, \mathbf{f}(1)=\frac{1}{2}\) Then the number of points of intersection of curve \(y=f(x)\) and the curve \(y=\) \(x^{2}-2 x-5\) is

1 1
2 0
3 2
4 infinite
AP EAMCET-2022-05.07.2022
Join With Us for More Updates
Limits, Continuity and Differentiability

80241 Let \(f(x)=15-|x-10| ; x \in R\). Then, the set of all values of \(x\), at which the function, \(g(x)=\) \(\mathbf{f}(\mathbf{f}(\mathbf{x}))\) is not differentiable, is

1 \(\{5,10,15,20\}\)
2 \(\{5,10,15\}\)
3 \(\{10\}\)
4 \(\{10,15\}\)
JEE Main-2019-09.4.2019
Limits, Continuity and Differentiability

80242 If \(f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; |x| \geq 1 \\ a x^{2}+b ;|x|\lt 1\end{array}\right.\) is differentiable at every point of the domain, then the values of a and \(b\) are respectively

1 \(\frac{1}{2}, \frac{1}{2}\)
2 \(\frac{1}{2},-\frac{3}{2}\)
3 \(\frac{5}{2},-\frac{3}{2}\)
4 \(-\frac{1}{2}, \frac{3}{2}\)
JEE Main-2021-18.03.2021
Limits, Continuity and Differentiability

80243 The function that is not differentiable at \(x=1\) is

1 \(f_{1}(\mathrm{x})=|\mathrm{x}|,-\infty\lt \mathrm{x}\lt \infty\)
2 \(f_{2}(\mathrm{x})=\left\{\begin{array}{cc}1+\sin (\mathrm{x}-1), -\infty\lt \mathrm{x} \leq 1 \\ \mathrm{x}, \mathrm{x} \geq 1\end{array}\right.\)
3 \(f_{3}(x)=\left(\begin{array}{c}x^{2}+7 x-7,-\infty\lt x \leq 1 \\ \frac{3 x-1}{2}, x \geq 1\end{array}\right.\)
4 \(f_{4}(\mathrm{x})=\left\{\begin{array}{c}|\mathrm{x}-1|+|\mathrm{x}-2|,-\infty\lt \mathrm{x} \leq 1 \\ 1+\mathrm{x}-\mathrm{x}^{3}, \mathrm{x} \geq 1\end{array}\right.\)
TS EAMCET-2018-07.05.2018
Limits, Continuity and Differentiability

80244 The function \(f(x)=\left|x^{2}-2 x-3\right| \cdot e^{\left|9 x^{2}-12 x+4\right|}\) is not differentiable at exactly

1 four points
2 three points
3 two points
4 one point
JEE Main-2021-31.08.2021
Limits, Continuity and Differentiability

80245 \(f: R \rightarrow R\) is a function such that
\(|\mathbf{f}(\mathbf{x})-\mathbf{f}(\mathbf{y})| \leq \frac{\mathbf{1}}{\mathbf{2}}|\mathbf{x}-\mathbf{y}| \forall \mathbf{x}, \mathbf{y} \in \mathbf{R}\) and \(\mathbf{f}^{\prime}(\mathbf{x}) \geq \frac{1}{2}\) \(\forall \mathbf{x} \in \mathbf{R}, \mathbf{f}(1)=\frac{1}{2}\) Then the number of points of intersection of curve \(y=f(x)\) and the curve \(y=\) \(x^{2}-2 x-5\) is

1 1
2 0
3 2
4 infinite
AP EAMCET-2022-05.07.2022
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Limits, Continuity and Differentiability

80241 Let \(f(x)=15-|x-10| ; x \in R\). Then, the set of all values of \(x\), at which the function, \(g(x)=\) \(\mathbf{f}(\mathbf{f}(\mathbf{x}))\) is not differentiable, is

1 \(\{5,10,15,20\}\)
2 \(\{5,10,15\}\)
3 \(\{10\}\)
4 \(\{10,15\}\)
JEE Main-2019-09.4.2019
Limits, Continuity and Differentiability

80242 If \(f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; |x| \geq 1 \\ a x^{2}+b ;|x|\lt 1\end{array}\right.\) is differentiable at every point of the domain, then the values of a and \(b\) are respectively

1 \(\frac{1}{2}, \frac{1}{2}\)
2 \(\frac{1}{2},-\frac{3}{2}\)
3 \(\frac{5}{2},-\frac{3}{2}\)
4 \(-\frac{1}{2}, \frac{3}{2}\)
JEE Main-2021-18.03.2021
Limits, Continuity and Differentiability

80243 The function that is not differentiable at \(x=1\) is

1 \(f_{1}(\mathrm{x})=|\mathrm{x}|,-\infty\lt \mathrm{x}\lt \infty\)
2 \(f_{2}(\mathrm{x})=\left\{\begin{array}{cc}1+\sin (\mathrm{x}-1), -\infty\lt \mathrm{x} \leq 1 \\ \mathrm{x}, \mathrm{x} \geq 1\end{array}\right.\)
3 \(f_{3}(x)=\left(\begin{array}{c}x^{2}+7 x-7,-\infty\lt x \leq 1 \\ \frac{3 x-1}{2}, x \geq 1\end{array}\right.\)
4 \(f_{4}(\mathrm{x})=\left\{\begin{array}{c}|\mathrm{x}-1|+|\mathrm{x}-2|,-\infty\lt \mathrm{x} \leq 1 \\ 1+\mathrm{x}-\mathrm{x}^{3}, \mathrm{x} \geq 1\end{array}\right.\)
TS EAMCET-2018-07.05.2018
Limits, Continuity and Differentiability

80244 The function \(f(x)=\left|x^{2}-2 x-3\right| \cdot e^{\left|9 x^{2}-12 x+4\right|}\) is not differentiable at exactly

1 four points
2 three points
3 two points
4 one point
JEE Main-2021-31.08.2021
Limits, Continuity and Differentiability

80245 \(f: R \rightarrow R\) is a function such that
\(|\mathbf{f}(\mathbf{x})-\mathbf{f}(\mathbf{y})| \leq \frac{\mathbf{1}}{\mathbf{2}}|\mathbf{x}-\mathbf{y}| \forall \mathbf{x}, \mathbf{y} \in \mathbf{R}\) and \(\mathbf{f}^{\prime}(\mathbf{x}) \geq \frac{1}{2}\) \(\forall \mathbf{x} \in \mathbf{R}, \mathbf{f}(1)=\frac{1}{2}\) Then the number of points of intersection of curve \(y=f(x)\) and the curve \(y=\) \(x^{2}-2 x-5\) is

1 1
2 0
3 2
4 infinite
AP EAMCET-2022-05.07.2022
NEET DIGITAL LIBRARY
Limits, Continuity and Differentiability

80241 Let \(f(x)=15-|x-10| ; x \in R\). Then, the set of all values of \(x\), at which the function, \(g(x)=\) \(\mathbf{f}(\mathbf{f}(\mathbf{x}))\) is not differentiable, is

1 \(\{5,10,15,20\}\)
2 \(\{5,10,15\}\)
3 \(\{10\}\)
4 \(\{10,15\}\)
JEE Main-2019-09.4.2019
Limits, Continuity and Differentiability

80242 If \(f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; |x| \geq 1 \\ a x^{2}+b ;|x|\lt 1\end{array}\right.\) is differentiable at every point of the domain, then the values of a and \(b\) are respectively

1 \(\frac{1}{2}, \frac{1}{2}\)
2 \(\frac{1}{2},-\frac{3}{2}\)
3 \(\frac{5}{2},-\frac{3}{2}\)
4 \(-\frac{1}{2}, \frac{3}{2}\)
JEE Main-2021-18.03.2021
Limits, Continuity and Differentiability

80243 The function that is not differentiable at \(x=1\) is

1 \(f_{1}(\mathrm{x})=|\mathrm{x}|,-\infty\lt \mathrm{x}\lt \infty\)
2 \(f_{2}(\mathrm{x})=\left\{\begin{array}{cc}1+\sin (\mathrm{x}-1), -\infty\lt \mathrm{x} \leq 1 \\ \mathrm{x}, \mathrm{x} \geq 1\end{array}\right.\)
3 \(f_{3}(x)=\left(\begin{array}{c}x^{2}+7 x-7,-\infty\lt x \leq 1 \\ \frac{3 x-1}{2}, x \geq 1\end{array}\right.\)
4 \(f_{4}(\mathrm{x})=\left\{\begin{array}{c}|\mathrm{x}-1|+|\mathrm{x}-2|,-\infty\lt \mathrm{x} \leq 1 \\ 1+\mathrm{x}-\mathrm{x}^{3}, \mathrm{x} \geq 1\end{array}\right.\)
TS EAMCET-2018-07.05.2018
Limits, Continuity and Differentiability

80244 The function \(f(x)=\left|x^{2}-2 x-3\right| \cdot e^{\left|9 x^{2}-12 x+4\right|}\) is not differentiable at exactly

1 four points
2 three points
3 two points
4 one point
JEE Main-2021-31.08.2021
Limits, Continuity and Differentiability

80245 \(f: R \rightarrow R\) is a function such that
\(|\mathbf{f}(\mathbf{x})-\mathbf{f}(\mathbf{y})| \leq \frac{\mathbf{1}}{\mathbf{2}}|\mathbf{x}-\mathbf{y}| \forall \mathbf{x}, \mathbf{y} \in \mathbf{R}\) and \(\mathbf{f}^{\prime}(\mathbf{x}) \geq \frac{1}{2}\) \(\forall \mathbf{x} \in \mathbf{R}, \mathbf{f}(1)=\frac{1}{2}\) Then the number of points of intersection of curve \(y=f(x)\) and the curve \(y=\) \(x^{2}-2 x-5\) is

1 1
2 0
3 2
4 infinite
AP EAMCET-2022-05.07.2022
Join With Us for More Updates
Limits, Continuity and Differentiability

80241 Let \(f(x)=15-|x-10| ; x \in R\). Then, the set of all values of \(x\), at which the function, \(g(x)=\) \(\mathbf{f}(\mathbf{f}(\mathbf{x}))\) is not differentiable, is

1 \(\{5,10,15,20\}\)
2 \(\{5,10,15\}\)
3 \(\{10\}\)
4 \(\{10,15\}\)
JEE Main-2019-09.4.2019
Limits, Continuity and Differentiability

80242 If \(f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} ; |x| \geq 1 \\ a x^{2}+b ;|x|\lt 1\end{array}\right.\) is differentiable at every point of the domain, then the values of a and \(b\) are respectively

1 \(\frac{1}{2}, \frac{1}{2}\)
2 \(\frac{1}{2},-\frac{3}{2}\)
3 \(\frac{5}{2},-\frac{3}{2}\)
4 \(-\frac{1}{2}, \frac{3}{2}\)
JEE Main-2021-18.03.2021
Limits, Continuity and Differentiability

80243 The function that is not differentiable at \(x=1\) is

1 \(f_{1}(\mathrm{x})=|\mathrm{x}|,-\infty\lt \mathrm{x}\lt \infty\)
2 \(f_{2}(\mathrm{x})=\left\{\begin{array}{cc}1+\sin (\mathrm{x}-1), -\infty\lt \mathrm{x} \leq 1 \\ \mathrm{x}, \mathrm{x} \geq 1\end{array}\right.\)
3 \(f_{3}(x)=\left(\begin{array}{c}x^{2}+7 x-7,-\infty\lt x \leq 1 \\ \frac{3 x-1}{2}, x \geq 1\end{array}\right.\)
4 \(f_{4}(\mathrm{x})=\left\{\begin{array}{c}|\mathrm{x}-1|+|\mathrm{x}-2|,-\infty\lt \mathrm{x} \leq 1 \\ 1+\mathrm{x}-\mathrm{x}^{3}, \mathrm{x} \geq 1\end{array}\right.\)
TS EAMCET-2018-07.05.2018
Limits, Continuity and Differentiability

80244 The function \(f(x)=\left|x^{2}-2 x-3\right| \cdot e^{\left|9 x^{2}-12 x+4\right|}\) is not differentiable at exactly

1 four points
2 three points
3 two points
4 one point
JEE Main-2021-31.08.2021
Limits, Continuity and Differentiability

80245 \(f: R \rightarrow R\) is a function such that
\(|\mathbf{f}(\mathbf{x})-\mathbf{f}(\mathbf{y})| \leq \frac{\mathbf{1}}{\mathbf{2}}|\mathbf{x}-\mathbf{y}| \forall \mathbf{x}, \mathbf{y} \in \mathbf{R}\) and \(\mathbf{f}^{\prime}(\mathbf{x}) \geq \frac{1}{2}\) \(\forall \mathbf{x} \in \mathbf{R}, \mathbf{f}(1)=\frac{1}{2}\) Then the number of points of intersection of curve \(y=f(x)\) and the curve \(y=\) \(x^{2}-2 x-5\) is

1 1
2 0
3 2
4 infinite
AP EAMCET-2022-05.07.2022