In which of the following functions is Rolles theorem applicable? `(a)f(x)={x ,0lt=x<1 0,x=1on[0,1]` `(b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0)` `(c)f(x)=(x^2-x-6)/(x-1)on[-2,3]` `(d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]`

Consider f(x)=|1-x| 1 lt=xlt=2 a n d g(x)=f(x)+bsinpi/2 x , 1 lt=xlt=2 Then which of the following is correct? Rolles theorem is applicable to both f, g a n d b = 3//2 LMVT is not applicable of f and Rolles theorem if applicable to g with b=1/2 LMVT is applicable to f and Rolles theorem is applicable to g with b = 1 Rolles theorem is not applicable to both f,g for any real b .

For the function f(x) = e^(cos x) , Rolle's theorem is applicable when

Explain why Rolle's theorem is not applicable to the following functions in the respective intervals. f(x)=tanx,x in[0,pi]

Explain why Rolle's theorem is not applicable to the following functions in the respective intervals. f(x)=|1/x|,x in[-1,1]

Show that Rolle's theorem is not applicable to the following functions in the specified intervals: f(x)={(x^(2)+1" when " 0 le x le 1),(3-x" when "1 lt x le 2):}

Show that Rolle's theorem is not applicable to the following functions in the specified intervals: f(x)=|x-1|" in " 0 le x le 2

Show that Rolle's theorem is not applicable to the following functions in the specified intervals: f(x)=tan x " in " 0 le x le pi