Medium
Let $f(x) = \begin{cases} \frac{x^p}{(\sin x)^q} & \text{if } 0 < x \leq \frac{\pi}{2} \\ 0 & \text{if } x = 0 \end{cases}$ where $p, q \in \mathbb{R}$. Then, Lagrange's Mean Value Theorem is applicable to $f(x)$ in the closed interval $[0, \frac{\pi}{2}]$ if:
- Afor all $p, q$
- Bonly when $p > q$
- Conly when $p < q$
- Dfor no value of $p, q$
Explore More
Similar Questions
Let $f: [-1, 2] \rightarrow R$ be a differentiable function such that $0 \le f'(t) \le 1$ for $t \in [-1, 0]$ and $-1 \le f'(t) \le 0$ for $t \in [0, 2]$. Then:
If $c$ is a point at which Rolle's theorem holds for the function $f(x) = \log_{e}\left(\frac{x^{2}+\alpha}{7x}\right)$ in the interval $[3, 4]$,where $\alpha \in R$,then $f''(c)$ is equal to
DifficultJEE MAIN 2020
View SolutionLet $f(x)=x^3+2x^2-x$ be a real-valued function. Then, the value of Lagrange's constant $C$ in $(-1,2)$ is
The function $f(x) = x^3 - 6x^2 + ax + b$ satisfies the conditions of Rolle's theorem in $[1, 3]$. Then the values of $a$ and $b$ are respectively
Let $f$ be a polynomial function defined on $[2,7]$. If $f(2)=3$ and $f^{\prime}(x) \leq 5$ for all $x$ in $(2,7)$,then the maximum possible value attained by $f$ at $x=7$ is
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo