Which of the following function can satisfy Rolle's theorem ?
Which of the following function can satisfy Rolle's theorem ?
- A
$f\left( x \right) = \left| {\operatorname{sgn} \left( x \right)} \right|in\left[ { - 1,1} \right]$
- B
$f\left( x \right) = 3{x^2} - 2\,in\left[ {2,3} \right]$
- C
$f\left( x \right) = \left| {x - 1} \right|\,in\left[ {0,2} \right]$
- D
$f\left( x \right) = \left( {x + \frac{1}{x}} \right)\,in\left[ {\frac{1}{3},3} \right]$
Similar Questions
For the function$x + {1 \over x},x \in [1,\,3]$, the value of $ c$ for the mean value theorem is
For the function$x + {1 \over x},x \in [1,\,3]$, the value of $ c$ for the mean value theorem is
Suppose that $f (0) = - 3$ and $f ' (x) \le 5$ for all values of $x$. Then the largest value which $f (2)$ can attain is
Suppose that $f (0) = - 3$ and $f ' (x) \le 5$ for all values of $x$. Then the largest value which $f (2)$ can attain is
Let $y = f (x)$ and $y = g (x)$ be two differentiable function in $[0,2]$ such that $f(0) = 3,$ $f(2) = 5$ , $g (0) = 1$ and $g(2) = 2$. If there exist atlellst one $c \in \left( {0,2} \right)$ such that $f'(c)=kg'(c)$,then $k$ must be
Let $y = f (x)$ and $y = g (x)$ be two differentiable function in $[0,2]$ such that $f(0) = 3,$ $f(2) = 5$ , $g (0) = 1$ and $g(2) = 2$. If there exist atlellst one $c \in \left( {0,2} \right)$ such that $f'(c)=kg'(c)$,then $k$ must be
lf Rolle's theorem holds for the function $f(x) =2x^3 + bx^2 + cx, x \in [-1, 1],$ at the point $x = \frac {1}{2},$ then $2b+ c$ equals
lf Rolle's theorem holds for the function $f(x) =2x^3 + bx^2 + cx, x \in [-1, 1],$ at the point $x = \frac {1}{2},$ then $2b+ c$ equals
- [JEE MAIN 2015]
A value of $c$ for which conclusion of Mean Value Theorem holds for the function $f\left( x \right) = \log x$ on the interval $[1,3]$ is
A value of $c$ for which conclusion of Mean Value Theorem holds for the function $f\left( x \right) = \log x$ on the interval $[1,3]$ is
- [AIEEE 2007]