Given: f(x)=4-((1/2)-x)2 / 3 g(x)= begincases( tan [x]/x), x ≠ 0 1 , x=0 endcases h ( x )= x k ( x )=5 log 2( x +3) then in [0,1], Lagranges Mean Value Theorem is NOT applicable to where [ x ] and x denotes the greatest integer and fraction part function.

Question

Given: f(x)=4-((1/2)-x)2 / 3 g(x)= begincases( tan [x]/x), x ≠ 0 1 , x=0 endcases h ( x )= x k ( x )=5 log 2( x +3) then in [0,1], Lagranges Mean Value Theorem is NOT applicable to where [ x ] and x denotes the greatest integer and fraction part function. (A) f, g, h (B) h, k (C) f, g (D) g , h , k

Tardigrade Admin · Accepted Answer

f is not differentiable at x=(1/2) g is not continuous in [0,1] at x=0 1 h is not continuous in [0,1] at x=1 k ( x )=( x +3) ln 2 5=( x +3) p where 2< p <3

Q. Given: $f (x) = 4 - (\frac{1}{2} - x)^{2/3} g (x) = {\frac{t a n [ x ]}{x}, 1, x \neq = 0 x = 0$
$h (x) = {x} k (x) = 5^{l o g_{2} (x + 3)}$ then in $[0, 1]$ , Lagranges Mean Value Theorem is NOT applicable to
where $[x]$ and ${x}$ denotes the greatest integer and fraction part function.

f, g, h

h, k

$f, g$

$g, h, k$

f is not differentiable at $x = \frac{1}{2}$
$g$ is not continuous in $[0, 1]$ at $x = 0$ & 1
$h$ is not continuous in $[0, 1]$ at $x = 1$
$k (x) = (x + 3)^{l n_{2} 5} = (x + 3)^{p}$ where $2 < p < 3$

Q. Given: f(x)=4−(21​−x)2/3g(x)={xtan[x]​,1,​x=0x=0​ h(x)={x}k(x)=5log2​(x+3) then in [0,1], Lagranges Mean Value Theorem is NOT applicable to where [x] and {x} denotes the greatest integer and fraction part function.