Rolle's theorem is true for the function $f(x) = {x^2} - 4 $ in the interval
Rolle's theorem is true for the function $f(x) = {x^2} - 4 $ in the interval
- A
$[-2, 0]$
- B
$[-2, 2]$
- C
$\left[ {0,\,{1 \over 2}} \right]$
- D
$[0,\,\,2]$
Similar Questions
If $c = \frac {1}{2}$ and $f(x) = 2x -x^2$ , then interval of $x$ in which $LMVT$, is applicable, is
If $c = \frac {1}{2}$ and $f(x) = 2x -x^2$ , then interval of $x$ in which $LMVT$, is applicable, is
Verify Mean Value Theorem for the function $f(x)=x^{2}$ in the interval $[2,4]$
Verify Mean Value Theorem for the function $f(x)=x^{2}$ in the interval $[2,4]$
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
Consider the function $f(x) = {e^{ - 2x}}$ $sin\, 2x$ over the interval $\left( {0,{\pi \over 2}} \right)$. A real number $c \in \left( {0,{\pi \over 2}} \right)\,,$ as guaranteed by Rolle’s theorem, such that $f'\,(c) = 0$ is
Consider the function $f(x) = {e^{ - 2x}}$ $sin\, 2x$ over the interval $\left( {0,{\pi \over 2}} \right)$. A real number $c \in \left( {0,{\pi \over 2}} \right)\,,$ as guaranteed by Rolle’s theorem, such that $f'\,(c) = 0$ is
Let $a > 0$ and $f$ be continuous in $[- a, a]$. Suppose that $f ' (x) $ exists and $f ' (x) \le 1$ for all $x \in (- a, a)$. If $f (a) = a$ and $f (- a) = - a$ then $f (0)$
Let $a > 0$ and $f$ be continuous in $[- a, a]$. Suppose that $f ' (x) $ exists and $f ' (x) \le 1$ for all $x \in (- a, a)$. If $f (a) = a$ and $f (- a) = - a$ then $f (0)$