Teachoo Quiz

Case Based MCQ Quiz

Chapter 5 Class 12 Continuity and Differentiability | 10 questions | about 8 minutes

Attempt time 0:00
This question 0:00
Question 1 of 10
Question 1 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
(i) Rolle's theorem is not applicable for the function \(\mathrm{f}(\mathrm{x})=\tan \mathrm{x}\) in \([0, \pi]\) because \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 2 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
The value of c satisfying Rolle's theorem for the function \(\mathrm{g}(\mathrm{x})=\sin \mathrm{x}\) in \([0, \pi]\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 3 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
The value of c satisfying Rolle's theorem for the function \(\mathrm{h}(\mathrm{x})= \cos x\) in \([0,2 \pi]\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 4 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
The value of c satisfying Rolle's theorem for the function \(p(x)=\sin x+\cos x\) in \([0, \pi]\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 5 of 10
Rolle s Theorem
Rolle s Theorem
Rolle's Theorem: Suppose following three condition hold for function \(\mathrm{y}=f(\mathrm{x})\) :
-1. function is defined and continuous on closed interval \([\mathrm{a}, \mathrm{b}]\);
-2. exists finite derivative \(f^{\prime}(x)\) on interval \((a, b)\);
-3. \(f(\mathrm{a})=f(\mathrm{~b})\).
then there exists point \(\mathrm{c}(\mathrm{a}<\mathrm{c}<\mathrm{b})\) such that \(f^{\prime}(\mathrm{c})=0\).

Based on the above information, answer any four of the following questions.
Rolle's theorem is not applicable for the function \(f(x)=|x|\) in [-2, 2] because \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 6 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
\(f \circ g(\mathrm{x})=\) \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 7 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
\(g \circ f(x)=\) \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 8 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
$$ \frac{d}{d x}\left(\sin ^3 x\right)= $$

\(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 9 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
$$ \frac{d}{d x}\left(\sin x^3\right) $$

\(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Question 10 of 10
Ms Remka of
Ms Remka of
Ms. Remka of city school is teaching chain rule to her students with the help of a flow-chart The chain rule says that if \(h\) and \(g\) are functions and \(f(x)=g(h(x))\), then
Based on the above information, answer any four of the following questions.
Let \(f(x)=\sin x\) and \(g(x)=x^3\)
\(\frac{d}{d x}(\sin 2 \mathrm{x})\) at \(\mathrm{x}=\frac{\pi}{2}\) is \(\_\_\_\_\) .
Select an option to see the answer, or skip this question.
Stuck? Keep your progress moving.