Let $f(x) = (x-4)(x-5)(x-6)(x-7)$ then -
$f'(x) = 0$ has four roots
Three roots of $f'(x) = 0$ lie in $(4, 5) \cup (5, 6) \cup (6, 7)$
The equation $f'(x) = 0$ has only one root
Three roots of $f'(x) = 0$ lie in $(3, 4) \cup (4, 5) \cup (5, 6)$
If $L.M.V.$ theorem is true for $f(x) = x(x-1)(x-2);\, x \in [0,\, 1/2]$ , then $C =$ ?
If function $f(x) = x(x + 3) e^{-x/2} ;$ satisfies the rolle's theorem in the interval $[-3, 0],$ then find $C$
Let $f(x) = \left\{ {\begin{array}{*{20}{c}}
{{x^2}\ln x,\,x > 0} \\
{0,\,\,\,\,\,\,\,\,\,\,\,\,\,x = 0}
\end{array}} \right\}$, Rolle’s theorem is applicable to $ f $ for $x \in [0,1]$, if $\alpha = $
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
If $f(x)$ = $sin^2x + xsin2x.logx$, then $f(x)$ = $0$ has